FL Geometry EOC Test Release 2025

Añadido: 2026-05-18

[00:00:02]Um, I know this is very late in your test, but we had gone over this in class and just some of you missed. So, I wanted to give you an opportunity to still uh hear how to go through these. This is the release state test um for for Florida, state of Florida, the geometry last year 2025 um released EOCC test items. There were 45 questions that they released and we're just going to go through the answers. The answer key was um is posted on on your team's page, but just so you can see how to do it. Um the answer key is nice that posts how many students got the question right and what was the um correct answer. So for number one, uh the triangle so two statements about triangle JKL are shown. So there's a triangle that exists and it has three points. The vertices are JK and L. They want to know which ratio represents costs.

[00:01:01]Um okay. So it's always good to draw a figure to see what the scenario is. Um if there's a triangle, we know it's a right triangle because of this first statement. So we know the right angle is L. And then it doesn't really give us information about where J and L uh K are located. So we can put them in either spot. Okay. So we can put them there. And then the um question tells us in the second piece of information that from J the sign um which is opposite over hypotenuse is 99. So the opposite of J is 99 and the hypotenuse of the triangle is 101. So we know that these two sides are true. So, we could figure out the last side if we wanted to by doing the Pythagorean theorem.

[00:01:52]And I'm not going to go through how to do that because you don't really need all of that in this problem. But if you did do that, the answer should come out to um 20 for the last side, which is where they're getting this 20 from in the answers. So hopefully you know how to do Pyagorean theorem, but you get a of 20.

[00:02:08]So this side is 20. So the question is asking what is the coine now, but from a different angle. So they've switched it up and now they're referencing from K.

[00:02:17]Well, the cosine from any angle is the adjacent side over the hypotenuse.

[00:02:23]So they want to know what is adjacent to K, which would be 99, and then what is the hypotenuse of the triangle, so it's B.

[00:02:37]Okay. Number two, um they give you a line segment and the line segments end points is again a diagram. It's going to help you even just place what kind of problem that these are. So line segment MN has end points um -7 10 and then 1 and point P is on line segment MN such that the ratio M to P is two parts and P to N is one part. So this would be divided into a total of three equal parts where are there are two parts before P and one part after P. So a 2:1 ratio. So we talked about in class that if these points M and N were playing tugof-war and P started in the middle, N is actually stronger because P ends up closer to N. So N is actually going to weigh more. So that's going to get the two So, we're going to put the two with there's two n's and there's only one m.

[00:03:41]Okay. And then it's really a weighted average problem. So, we're going to um write n twice and m's coordinates just once and then we're going to add those and average those. So, average means adding up the numbers and dividing by how many numbers you added. So, -3 and 12 would both be divided by three because there are three numbers in the set. to to yield that P would land at -3 4.

[00:04:11]Okay, they don't really care about where the y coordinate is, but the x coordinate would be3.

[00:04:19]Okay, number three. Um, which statement is true when a threedimensional figure is dilated by a given scale factor?

[00:04:31]Um so a dilation of a scale factor that is between zero and one is a reduction and if the scale factor is greater than one it's getting larger.

[00:04:46]Okay so they want you to understand that so a dilation of a scale factor of 2/3 which is really 0.6 repeating which is between this range should have been a reduction. So this is incorrect.

[00:04:58]A dilation of 0.1 is also in this first range. So it should have been a reduction.

[00:05:08]Um 3 / 2 is really 1.5. So this should have been an enlargement increase.

[00:05:18]And then 3.5 is bigger than one. So this is an increase. So this is the one that is true.

[00:05:28]Okay, number four is um if two lines are cut by a transversal um what are the values of x and y? So we talked about anytime two lines are cut parallel lines they have to be parallel are cut by a transversal. There are four spots that are the same. These four are the same kind of alternates. The other four that are the same would be these spots.

[00:05:54]If they're not in the same spot, then they have to make 180. So there's only ever two cases. So either the two spots are equal or the two spots add to equal 180 if you only have two sets of lines in a transversal.

[00:06:06]So if we look at the map here, 94 and this, they are in the same in in a marking that's the same. They're both in these like little slash markings. So these are alternate interior, which are equal when lines are parallel.

[00:06:19]Okay? So these would be equal. So 94 is equal to x + y. So these spots would be equal. These two spots that are next to each other, these are called same side or consecutive interior are not the same. Two different markings means they add to equal 180. So this means that 94 and x should equal 180.

[00:06:43]Okay. So we have to solve this one first. So we subtract 94 from both sides to get that x is equal to 86. And then we can plug in 86 here and solve this one for y.

[00:07:00]Uh 4 + 4 so 8. So x will be 86 and y will be 8.

[00:07:09]Okay. So again um this is really making sure that you understand what is congruent on when parallel lines cut are cut by a transversal and that um you understand alternate interior and consecutive interior. Alternate interior are equal when lines are parallel and consecutive interior are supplementary which means they add up to equal 180 when lines are parallel.

[00:07:40]Okay, number five. Um, these properties give people these quadrilaterals give students a hard time, but if you visualize, and I'm on my tablet, so I'm not it's not I'm not great with writing on these, but if you visualize a parallelogram, a parallelogram by definition has to have the parallel opposite sides. Okay? And you can draw parallelograms kind of a lot of different ways. So you can draw it really skinny, you can make it like this.

[00:08:07]Um you can draw them.

[00:08:11]Yes. More like this where these um it's like flatter.

[00:08:19]Okay. So the diagonals are congruent. So um it's sometimes hard to tell but on this one for example you can tell that this is going to be shorter than this way. Although these sides are still parallel. Um but the diagonals if you can visualize even if you didn't memorize the properties you can still sometimes get these.

[00:08:37]All right. Um this the second one that I drew is a little more clear that the diagonals if I were to connect this and this that the diagonals will not be 90°. These are going to be acute and obese singles. Um opposite angles are equal to 90. Um this angle and this angle are already each bigger than 90.

[00:08:54]So we already know that this is not true. And then the consecutive angles are equal to 180. This goes back to understanding that with parallel lines cut by a transversal, consecutive interior are supplementary. So it's really similar to what we just did in that other problem where these would be consecutive interior on a parallelogram if you only drew one side of the parallelogram and then the parallel side. So three sides of it. You can see that these are consecutive interior. So they must be supplementary. Okay. So it's going to be D.

[00:09:27]Okay. And number six is you just memorizing the vocab. Do you know what converse, inverse, and contraositive are? Period. Okay. So the original statement is if A then B.

[00:09:37]A and B are statements. The converse exchanges them. So it says if B then A.

[00:09:46]The inverse keeps the original conditionals order but changes the um statement to not to include not. So it inverts the statement. And then contraositive is the longest word. So it does the most. It changes them to um not and it puts the second part of the original statement first.

[00:10:13]Okay. So um it should be contraositive um converse and then inverse.

[00:10:24]Not going to spend a lot of time on that cuz if you know the vocab you either know the vocab on this or you just don't know it. So you got to learn you got to um study over that and know for the test.

[00:10:35]All right. This one is a one that you would draw. So, you would plot the points 2060 24Q.

[00:10:44]Okay, I'm going to go ahead and try to plot these really quick. Um 206 QRS.

[00:10:51]All right, I'll just plot it on this one because we're right here.

[00:10:57]Okay, so you would want to plot this and they are going to provide you graph paper two.

[00:11:02]I forgot Sorry. Let me just write it on a separate sheet of paper and I'll come back to Oh, you know what? I have another paper in front of me. So, let me go to the graph. Okay.

[00:11:20]I never found that page.

[00:11:23]I have a hard copy in front of me. So, okay. Q is two 0. Um, R is 6.

[00:11:34]and then s is 24 and they make a triangle. They tell you that they are vertices of a triangle.

[00:11:42]Then it says that t is 8 0 u is 4 4 and v is 4 0.

[00:11:58]All right, bear with me on the graph.

[00:11:59]Yours should be straight hopefully. Um, okay. So, which statements, the question wanted to know which statements describe the relationships between the first and second triangle.

[00:12:09]So, we need to see if they are um they're asking if they're congruent or if they're similar. Um, so this side, if we count it, it's four units. This side is four units. And we know that it's a right angle because it's made of four vertical and horizontal lines. So, this side is also four units. And so is this side BT. And this is a right angle as well. So we know because of side angle side they have two sides and the angle between them in common that they are congruent. Okay. So they have two equal sides and the angle congrent. So we know it's between A and B. Then we need to see if Q goes with P or V basically. Okay. So Q is the right angle and V is the right angle. So the right angles need to match. So Q goes with V.

[00:12:58]So we know that this point has to map on to this point.

[00:13:03]All right. So then they want to know in part B what transformations will do that.

[00:13:08]So if we take Q and we shift this whole picture um it looks like if okay so you kind of have to this is why we did all those transformations and combinations where you have to do multiple transformations in one step. But it looks like if you translate this over by two units, QST will land here.

[00:13:32]Then if you take that and flip it down, um, it would land here. So, it's going to be a translation of two units to the right, which means x + 2, and then a reflection across the y uh the x axis is going to change the y sign. So, this is how you write the rule. So, we're moving everything right two and then flipping it across the x-axis, which makes the y-coordinate. Let's say the y coordinate was 44. It makes it now, sorry, 44.

[00:14:07]It makes it now 44.

[00:14:13]Okay. So, it takes the original and just changes the sign for the y.

[00:14:27]Okay. So, I had to do most of the work on a graph. So, that one is um that's it. So, this one should have been Q was the ver and V were the right angles. So B and then we had a shift two. So the translation is a shift of two and then we can reflect it across the X which is a change in the Y sign.

[00:14:58]Okay. So the circles properties you just have to remember there's a lot of them and they're not on the formula sheet at all for you. So, um, so I did post on your, um, module 11. Hopefully, if you were here the last couple days, you saw the markup of the formula sheet.

[00:15:19]Oh, it got shifted down a little bit.

[00:15:20]Let me take let me do a different classes because this one, it looks like my pen got shifted. So, let's look at um, maybe first period.

[00:15:32]Okay. So, in the reference sheet, um, again, I wrote all these circles formulas.

[00:15:41]So, you want to make sure you take a snap a picture of that, um, to study over. Hopefully, you wrote this on your formula sheet like the rest of us. But if you didn't didn't do a sign picture of that so you can see how the central angle or the inscribed angle or it an angle that's inside the circle but not the central how they all relate in a formula.

[00:16:02]So um I'll just go ahead and do this one. But that's what that's the what the knowledge that they're expecting you to have when you're doing this one um in front of you. Okay. So indescribed angle and the central angle. So this if this is x that means the ark that it opens up to is x there the central angle is equivalent to the ark.

[00:16:24]If this is y the y which is the angle is equal to half of the ark.

[00:16:31]So the angle which is y is equal to a half of the ark that it opens up to. So y is opening up to x. So it's half of x.

[00:16:37]You just drop in x for the ark, y for the angle. So that's the answer. yals a half of x. Or another way to write this if you multiply both sides by two is 2 y = the twos will cancel equals x.

[00:16:53]So you could write this or 2 y = x is also an acceptable answer um for that.

[00:17:03]Okay. Number nine is um a figure is drawn on the credit plane. The transformations are performed.

[00:17:10]Okay. So they're asking about congruent or non- congrent. So the only types of congruent the most of the congruent the transformations are congruent. Um translations, reflections and rotations all result in congruent figures. Non-ongruent figures are the dilations. Those are the ones that are changing size. But these other ones are transformation are congruent transformations. So if it has a multiplier, it's like a k the scale factors multiplying the coordinates by something. Those are not saying the same size unless it's multiplying by one.

[00:17:45]That's the only case where it stays the same size. But if there's multiplying by anything besides one, it's changing size. Nothing else has a multiplier in front of it. And they're all reflections or rotations. This one would be a rotation. If you were to actually pick a test point like 1 3 and then you graphed it, you can see that this would turn into 31.

[00:18:12]So it just turned 90° clockwise.

[00:18:17]So it's also a rotation. So all of these would be congrent. Only the multiplier one would be non- congrent.

[00:18:29]Okay, number 10 is a line segment has end points at 1, one and a midpoint of 1,3.

[00:18:38]What are the coordinates of the other end point? Okay, this is just skip counting. So if we look at the x coordinates, if you are skip counting ever, if you're finding numbers in a sequence, they are all evenly spaced um if they're if they're in a arithmetic se sequence. So it's going from one to one. So, it's going to be at one still. It's not even It's an increase of zero. So, you don't increase anything. It's still just zero.

[00:19:04]For the y-coordinates, it's going from 1 to -3. So, it's skip counting by decreasing by four.

[00:19:11]So, it's decreasing by four. So, we would start off at -3 and decrease by four. And the answer would be negative 1g7.

[00:19:30]Okay, number 11.

[00:19:33]If you watch the math shorts video, these are super clear.

[00:19:39]Um, I think it's called like 3D.

[00:19:45]Let me just see what it's called. Pretty sure it's like um Ninja.

[00:19:59]Um yes, it's called Math Shorts episode 8, but it's some math shorts episode 8.

[00:20:19]Sorry. Um, so if you just if you just YouTube if you're not sure how to do these, but the visual is really helpful. Ninja 3D crosssections, it's the first link that comes up. Um, it's a one and a half minute video. It's really short and it just shows you what the cross-sections mean. It's really well explained on there, but my drawings are just not going to do it justice. So, um, the top would be a trapezoid. This little piece would be a trapezoid.

[00:20:53]So, again, if you cut this and remove it, you would see this shape at the top and then on the bottom you would see this, you know, rectangle.

[00:21:06]Okay, seems to Okay, so they have some points. I got to find this one on here.

[00:21:10]So number 12 I'll plot it and then I'll do the slopes.

[00:21:17]So all right so we'll plot um so let's just go ahead and plot these are all positive they're all in the first and um fourth quadrant. Okay so I'll just make my graph start like this. All right. So, T is at 25.

[00:21:45]U is at 66 3 and V is at 4 -3.

[00:22:02]All right. So from mine, you wouldn't be able to tell if it was a right triangle or not, but it says completely the same as to explain why triangle TV is a right triangle. So they're telling you it is a right triangle. So they want you to come up with the slope of t to you first. So slope, it's on the formula sheet, so you can just use the formula on the formula sheet, which is y2 - y1 over x2 - x1.

[00:22:23]But that's kind of tedious. So you can count the rise and the run. So from t to u it rises one and then it runs 1 2 3 4.

[00:22:34]So the slope is 1/4.

[00:22:37]The slope from t to v is a rise of 1 2 3 4 5 6 8 rise of eight and a run of one two to the left which is a negative. So if you move left remember it's negative or if you move down it's negative. Okay.

[00:22:56]So that simplifies to -4 over 1 or -4.

[00:23:03]So because these are opposite signs and reciprocals, this would be a a right triangle. So perpendicular. So remember perpendicular slopes have to have opposite signs and reciprocals.

[00:23:15]Um so again if you get a slope of something like 1/4 then if it's a perpendicular line the other slope is going to be4 1 which is really4.

[00:23:30]Um so a slope of 2/3 for example would mean need a slope of 3 negative to be perpendicular.

[00:23:40]uh a slope of 57th negative would need a slope of 7 fths for perpendicular.

[00:23:47]Okay, but this is just making sure you understand that perpendicular lines have opposite reciprocal slopes.

[00:23:57]All right, 13. Back to circles. So knowing the circle properties is essential. This is an inscribed angle.

[00:24:03]So the angle is going all the way the vertex of the angle's on the circle. So the angle's a half of the arc. So the angle the other way you can think of the angle as half of the ark is saying that 2 * the angle equals the ark. These are the same formula but rearranged. So I can move this multiply this whole thing by 2. Multiply this whole thing by two.

[00:24:25]It cancels with the 1/2. So the ark is equal to 2 * the angle. So we just drop the angle in 2x - 6 and the ark.

[00:24:34]And then solve algebra.

[00:24:39]Okay, just pause it if you need to to do the algebra, but um getting 28. Okay, then they ask for the measure of ABC. So they want us to plug it into this one.

[00:24:50]So tsing by 28 and then subtracting 6. 2 * 28 is 56 - 6 is 50.

[00:25:01]So 50 would be the measure of angle ABC.

[00:25:11]Okay. 14. The cone has a radius of three, a height of four.

[00:25:20]Sorry y'all. Really not good with this.

[00:25:23]And a slant height of five.

[00:25:34]Okay, find the surface area. So, the formula sheet has the surface area for um any threedimensional shape.

[00:25:42]So, you want to find the cone. It tells you what shape it is so that there's no guesswork there. And then there are two formulas on the formula sheet for surface area.

[00:25:50]B + pi rhs.

[00:25:54]And the second one is the same formula, but instead of calling the slant height HS, they call it L. So whichever one you prefer, C.

[00:26:02]So the B, remember for B, you want to draw anything that's capitalized. You want to draw the base shape in isolation.

[00:26:09]So the B here would be the area of the base shape. So the area of a circle.

[00:26:15]Okay, that's also on the formula sheet.

[00:26:16]So the area of a circle is pi r 2.

[00:26:21]So we're doing pi 3^ squar for the b.

[00:26:28]So that's 9 pi plus pi the radius was three and the slanted height was 5. So you didn't even need this four in the problem at all. It's just extra information.

[00:26:41]But if you multiply these it's 15 pi.

[00:26:44]And if you notice all the answers in terms of pi. So you don't want to actually multiply the pi. You just want to multip you just want to add the coefficients. So 24 pi would be the in terms of pi surface area. Um 13.

[00:27:09]All right. So rectangle blah blah ABC has a side length given side lengths. AB is five and BC is 11. If you want to draw a picture again, it's helpful.

[00:27:19]Remember, when you're naming these shapes, you want to start in one corner and move clockwise or counterclockwise around the figure. You don't ever want to cut through when you name it. So, A B C D.

[00:27:30]Okay. So, mine's not drawn a scale because I should have drawn AB longer.

[00:27:34]So, I could either just redraw it.

[00:27:40]So, A B C D if I wanted to be a little more to scale. So AB is 5 and BC is 11.

[00:27:49]They're saying that P QRS is congruent to this. So in congruent figures, the way that they name it is super important. So QR is written in the middle, second and third. So it would be matching up with BC, which is written second and third. And BC was 11.

[00:28:10]If they're congruent, then H then QR would also be 11.

[00:28:18]Okay, this one um has a really good video as well. So on the team's page, if you um just watch these, these are like less than five minute little clips of videos, but they visually show you what's happening on these figures. So what's happening on this one is you're rotating this figure around a vertical line. So it's going to end up being a three-dimensional figure that looks like a.

[00:28:43]Okay, so these are not hard questions, but you just need to see the visual on the if you just see the videos um if you are absent you want to watch those videos and then you'll be fine. Okay, construction of a perpendicular bis sector. Um we've done constructions a lot on the um delta math. So hopefully by now um you can kind of see this first one is constructing an angle bis sector.

[00:29:08]So it's cutting an angle in half.

[00:29:11]The second one is well it's going to be C. So remember our steps to construct a perpendicular bis sector. It means we want to find the middle of this and we want to cut it exactly at like the we want the we draw the line so that it makes a right angle. So we make a circle around this first one that is you know whatever size. Then we make the same size circle around this one and then where they intersect is the perpendicular bis sector. All right. So it's just C. But that one with the tools on on delta should be pretty straightforward.

[00:29:46]Okay. Another question again. If you watch those videos, those visual videos, this one shouldn't be too difficult to see um what kind of shape it is. So there would be a hole in the middle, but it would take on the shape of um letter D. Okay. So again, these are give me questions if you watch the video. If you're absent all the time and you missed it, you do want to go back and make sure you check the daily agenda and and watch the videos that you missed.

[00:30:11]Um, most of the state will get those kind rights. So, if you're not getting those right, you're missing some of the easier points on the test. Okay. Triangle has uh triangle M.

[00:30:24]Interesting that they name it with one letter. So, triangle M, we'll just call it triangle M. Has a base length of 18 and a height of 12. And now I drew it as a right triangle, but you don't have to.

[00:30:36]I do know that the base and the height, so even if you drew it like this, their base and the height are still 12 and 18 for M. And they're saying that triangle N is congruent. So what's the area of the triangle? So the area formula is not one that they're going to put on the formula sheet for you. You just have to know that it's area is equal to half the base times the height.

[00:30:56]And then this is a pretty getable question. So, not necessarily hard, just matter of you knowing the formula for area is 1/2 the base times the height.

[00:31:06]Let's see how many people got that right mistake. So, that's uh that's going to be 9 * 12. So, 108 wow 34%. That's kind of because they don't put the formula on the form. I think it's mainly because they don't put the formula on the formula sheet. If they put the triangle formula, then it'd be no problem, but they don't. So you do have to memorize this triangle formula.

[00:31:27]And remember the hint is that it's if you know the rectangle formula is base time height, which most people do can figure out. A triangle is half of that.

[00:31:35]So you slice it in half. So you take half of the rectangle's area, which is the base height.

[00:31:43]All right. Then we get into these circles questions. So so far we've seen several circles. One, two, three. Um at least three circles questions.

[00:31:52]um going back through. Yeah, three circles questions it looks like, but they're going to amp it up. There's going to be some more in the end, but these are some of these are gimme questions, but it's just a lot of formulas to remember. So, the center is the opposite sign. So, you look at these numbers and you change the sign. So, it's going to be 1 -4 is the center. And if you know that, you don't even need to know how to do the end of the question. So 14 is the center is the um only option that that's even the center of the circle of is a.

[00:32:25]Okay. Now the second part of this is the radius squared. So if you're trying to find the radius you would square root both sides and 12.25 square root is 3 3 and 1/2. So the radius should be approximately 3 and 1/2 based on the picture. And this one does show one two three and then half of a unit. Okay. So it's this first one a another circles question. So on four four circles question so far but again it should be a lot of circles a lot of threedimensional.

[00:33:04]So module 10 module 11 and then transformations and then a lot of things with coordinate geometry. So missing in point slope um length of a segment things like that.

[00:33:21]Okay. So the measure of arc AC is 28 and circle um a circle with chord AB is perpendicular. So this is these are evenly spaced. That is significant because that means that these slices are equal. So because um this it says it's perpendicular. So this is a right angle and this is the same because of reflexive property. These triangles would be congruent by side angle side making this angle equal to this angle by corresponding parts and these are both 28.

[00:33:54]All right. Then the rest of the circle they want to know BD. Well this is the diameter it's going through the middle of the circle. This would be 180°.

[00:34:12]So if we do we only we want to take away this 28 because 28 of it is B to C but we want the rest of it. So it's just 180 minus 28.

[00:34:21]So the circles questions aren't going to take you a ton of time but you just either know how to that the circles you know either know the properties or you just don't know them. Okay. But I would say study over those properties. Um, okay. This one says triangle, you know, XYZ is transformed.

[00:34:42]So, they're telling you it's a translation because of this the way the rule is written. So, this is a translation and they want to know what did they move it like which direction. So, three goes to one. So, that means it's like moving left versus right. They can either move left or right for the x coordinate. It's moving left four units and then so again three to get to negative 1. If you're not sure you would just graph this 2.

[00:35:15]So you would then count 1 2 3 4. So it moved left four. So4 for B. And then it moves from 2 -2 to 5 is up seven.

[00:35:25]But again just just count it if you're not sure if you're not good with integers adding and subtracting them.

[00:35:30]just graph them and count it. The whole figure is moving every point. So, they're all moving the same amount. Um, let me see what percentage of the state.

[00:35:40]Okay, less than half. But if you just plot this, um, there's no reason that you shouldn't be able to get it right.

[00:35:46]Okay, so number 23.

[00:35:50]A tile is in the shape of a trapezoid.

[00:35:53]The tile is divided into two parts by its mid segment.

[00:35:56]What is the area? Okay, the area of a trapezoid is on the formula sheet. So that's nice. Area is 1/2 height time base 1 plus base 2. The bases are your parallel sides and the height the vertical distance between the parallel sides or the sorry the perpendicular distance between the parallel sides. Okay. So the top part is shaded. What is the area of the shaded part? All right. So because this is a mid segment, they tell us that. That means the length of this middle segment is directly in between in the middle of 6 and 12. So we're looking to see what's the middle number between 6 and 12. So if we look at the full jump being 6 units, we're just going to go halfway to figure out the middle of this is nine.

[00:36:45]Okay. So this trapezoid has a height of it's the middle segment. So if the height was originally four, now the height is two. Sorry, that's supposed to be straight perpendicular two.

[00:37:00]Having trouble on this tablet two.

[00:37:04]Okay. So then you're just plugging in two. Okay, sorry. Half 2 six and 9.

[00:37:12]So half of two is 1 and 6 + 9 is 15. So 15 would be the answer.

[00:37:24]Okay, these are um again this this is a hard test because there's a lot to remember like this is on the formula sheet luckily but um but there are some things like part parts of this problem like mid segment you have to remember that it's the middle length the length of the segment is the middle length between these parallel sides. So all of that stuff makes it a difficult problem.

[00:37:43]Um where 37% of the state got it last year or yeah last year. So it it's not difficult if they had given you the regular figure as a trap but they throw a little bit of a you know terminology you have to know in there by doing things like making sure you're familiar with midsegment.

[00:38:04]Okay. Asles trapezoid is shown. So trapezoids by definition have one pair at least one pair. Some of the resources define it of parallel sides.

[00:38:19]Okay, so these are the ones that look parallel. So we're going to go with those being the parallel since the trapezoid in one set has to be parallel.

[00:38:26]Okay, so if it's an isosles, it means it's symmetric down the middle of the figure. So this corner is 2x + 6 and this corner is x.

[00:38:38]Um because the sides that are not parallel are going to be equal. So it's going to be like a symmetrical figure um across this line. Okay. So if you have lines two parallel lines cut by a transversal couple problems so far on this. So this is the third one what we've seen where they're really testing to make sure you know those relationships among parallel lines and transversals. So these are consecutive interior and should therefore equal to add to equal 180.

[00:39:10]Okay. And then we're going to solve this for x by subtracting 6 and then dividing by three. So let's see what that is.

[00:39:21]58.

[00:39:24]Okay. Then they want to know the measure of h i j. Okay, so they want to know the measure of this one.

[00:39:32]So if we plug in 2 * 58 286 so that's 122.

[00:39:46]So the quadrilaterals unit is really was a really challenging unit for a lot of you because there's a ton of properties that you have to remember. But if you can visualize this shape, I do think that will help you with some of the properties. Now, there's still going to be some memorization that's involved, but um but some of the properties will will come come to you.

[00:40:06]All right, what time are we at? Okay, 40 minutes.

[00:40:09]All right, rectangle G has a length of 15.

[00:40:24]Okay. and um a width of 20. Rectangle H is similar and has a length of 18 ft.

[00:40:31]What is the width?

[00:40:35]Okay, so if similar figures are similar, their sides are no longer equal. You can already tell the lengths are not equal, but they are proportional. So 15 is to 18. Whatever ratio that's in, 20 and x need to be in the same ratio. And then we butterfly me this out. Cross multiply to solve. So 2 * 18 is 36. Add a zero.

[00:40:54]And then divide by 15.

[00:40:59]24.

[00:41:10]All righty.

[00:41:14]Another parallel line and transversals.

[00:41:16]So we're seeing five four so far.

[00:41:18]Parallel lines and transversals. Got to know those angle relationships. So if this is 32 without even reading the problem I already know these all should be 32 in these spots if these lines are parallel.

[00:41:29]Okay. Angles PQR and PQR. So this 32 and QH J this one are congruent. They're both 32 because they are corresponding. They're in the matching position. So if you were to take this vertex and pick it up, put it on translate at the top of this one, these would match. So this is 32.

[00:41:54]Okay, that's it.

[00:41:58]Select all the true statements. Okay. Is ax equal to b y? Not necessarily. They have different markings. So if they were both two sticks, then they would be the same, but that's not necessarily true.

[00:42:09]dx is congrent to c y. Okay, for the same reason, that's not necessarily true. XY is parallel to CD.

[00:42:18]Okay, they did tell us it's a trapezoid.

[00:42:20]So these sides are parallel, which means this is a midsegment because it's created by the midpoint of this side and the midpoint of this side. It would also be parallel um to the bases and it would be half of the lengths of the bases. So it's the middle segment. So you average you add and divide by two. So this is also true.

[00:42:41]Trapezoid AB X.

[00:42:46]No, these aren't the same size. You can tell the um bottom one's a little bit bigger. So, it's just this just Cindy.

[00:42:57]Okay. Number 28.

[00:43:04]Regular pentagon pent is shown a slight height.

[00:43:09]Okay. Which expression represents a surface? So, you have to figure out from the formula sheet what um shape this is.

[00:43:17]Well, it tells you actually, so you don't have to figure it out. So, service area of a of a pyramid on your formula sheet, the service area of a pyramid is given as B + 12 PHs.

[00:43:31]Um, whenever you see a B, a capital letter, you're going to basically look at the base shapes area. So, this is the area of a um regular pentagon, which on the formula sheet, they call it a regular polygon because they want to make sure they include all the types. It could be four.

[00:43:47]It can be any amount of sides as long as they're all the same amount to be regular. The same size, I mean. Okay.

[00:43:54]So, the formula for that is 1/2 PA. I'm just looking, this is directly from the formula sheet.

[00:43:59]So, the P is the perimeter. So, we would look at the perimeter of this, which is if these are regular, that means there's these are all six. So, the perimeter would be 30 or 6 * 5.

[00:44:12]And the apothem is the segment connecting the center to the middle of a side. So this is 4.

[00:44:18]So half of 30 is 15 * 4 is 60. So the b is 60.

[00:44:25]Okay. I'm looking at these answer choices and they don't have a full answer. So I'm going to leave it as in the base form. I'm going to put it as 12 34 + 12.

[00:44:38]P means the perimeter of the base. So we already actually found it here was 30 and then um HS is the slant the height of the slant. So this all these letters are they tell you on the key what they mean on the formula sheet. So you just have to like read it and then but the capital letters you do have to know that it means for this base shape here specifically. Okay. So SL1.

[00:45:01]All right. So let's look at our choices to analyze which one is correct.

[00:45:06]Um, so I see a six in all the choices and none of the choices have So all the choices have six in them. So they want us to factor out a six if we can out of this. So I'm going to recopy this. 12 30 4 a half 30 and 11.

[00:45:25]All right. So if I factor out a six here, I'm left with five in the inside on this one. If I factor out a six here, I'm also left with five.

[00:45:37]These are um alike. This part of the for plus and this part of the formula are alike, which means you can factor that out. So um it's really like the reverse of the distributive property. We're undistributing the 6 * the 5 so that we're left with 4 + 11 in the parenthesis.

[00:46:01]And then um they just wrote it as 6 * 5 over 2. This is the same thing as this.

[00:46:07]So it's this last one. Um if you wanted to, you could just evaluate the answers for each of these. So you could type in 6 * 11 * 5 / 2 and that's like 165.

[00:46:22]And you can do the same thing with every answer choice. Um once you do that then you would see which one matches your final answer.

[00:46:36]Okay. So a little more timeconuming but but still getable for the answer.

[00:46:42]Um so this one's 225 if I did it all the way out. So then I could just type this in. This one should be 225, but I'll just double check it. And then 11 / 4 * 11 by 222 * 11. This one's 242.

[00:47:05]And then 5 * 55 / 2 + 4 = * 6, it's 189.

[00:47:13]So they even put the answers in like size order. But if that if what they try to do for the answers confuses you, just solve it all the way out and then solve all these answer choices out and see which ones match.

[00:47:39]Okay, so Ashley draws a map of her tongue where each map represents a mile.

[00:47:42]Okay. So, basically they're just looking to see like wherever her pizza is or the pizza shop is like at 67. So, it's like around here is the pizza shop and she's located at like 93.

[00:47:59]She wants to see if she's in a 6 mile radius.

[00:48:04]So, 6 mile radius of the pizza shop. Is she going to fall in it or not? So, you just need to make sure that her distance is less than six miles.

[00:48:13]or equal to six miles. Well, it says within so less than six miles. So, we just need to see if this is less than six. When you do the distance formula between these two points, um the formula sheet has the state has x2 - x1. So, I'll do 6 - 9^ 2 and y - 3^ 2.

[00:48:38]3^ 2 is 9.

[00:48:41]or squared is 16.

[00:48:44]So her shop is only five miles away is 5 miles radius from the pizza shop which is less than six.

[00:48:52]So yes like she can hers will pizza shop will deliver to her house.

[00:49:07]Okay, kind of claims the sum of any of the interior angles of any closed figure is 360 degrees or greater.

[00:49:15]Um, the sum of the angles of a triangle is 180. The sum of the angles of a quadrilateral is 360. Sum of the angles of every time you add a side it adds another 180.

[00:49:26]So, um, so basically, if you want to prove her wrong, a counter example, you just need to draw a triangle. It doesn't really matter what kind of triangle, but just needs to have three sides because the sum of those angles would be equal to um it would be equal to 180.

[00:49:57]Okay, another circle question. So on five for the circles. So in a quadrilateral ADC is okay. Opposite angles. So this is a circle property that you just have to know. But the two in a quadrilateral I'm sorry in a circle specifically the quadrilaterals opposite angles in this case B and D are supplementary. And it's just a a theorem that is easiest to memorize. Um the reason hanging has to do with inscribed angles equaling half of the arcs. Um and the two arcs equaling 360.

[00:50:35]So they're opposite inscribed angles which are opening up to the opposite sides of the arcs is half of that. But I mean to me that's more complicated than just memorizing the rules. So supplementary meaning a DC should be 180us 82 or 98.

[00:50:54]The next one has the circles tangent.

[00:50:59]So these would be the same because of t.

[00:51:02]Okay. So if they're tangent that means that the triangles we already know radiuses are the same and they tell you here because they both put x. This is the same because it's the reflexive property. FH is the same as itself. So these are congruent by hypotenuse leg.

[00:51:15]Therefore their corresponding parts are congrent. So you could set these equal.

[00:51:24]and then you have to solve it. Okay, so they want you to solve it out. So 4x - 10, you would solve it by setting it equal.

[00:51:32]Subtracting 4x, you get -2x. So x is 5.

[00:51:37]Um, all right. A right triangle is shown.

[00:51:49]Select the expression for the rat the trig ratio for the triangle tangent 30.

[00:51:55]Okay. So tangent is um opposite over adjacent. So they said from the 30° angle they want the tangent. Opposite would be 7 over 40 41 7 over<unk> of 41. And in the adjacent we don't have. So we need to do the pagorean theorem.

[00:52:17]Actually because it's a 30 609 we could use special rights here. So remember on 30 6090 it's going to be faster to use special rights. So this is x. This is x radle 3 and this is 2x. So if the x side in this case the x side is 7 radical 41 then the x radical 3 side means you plug in 7 radical 41 for x and then just bring down the radical 3. That's 7 radical 3 * 41.

[00:52:50]So it's three um 123. So 7 radical 123.

[00:52:57]Okay. So they have it in. So they actually want you to do special right triangles because the answers are all in radical format. So the opposite is 7 over 7 radical 41. The adjacent is 7 radical 123.

[00:53:16]Okay. Select all the figures that have a triangular cross-section when sliced parallel to the base. So the bases are the um we shaded the bases when we did this assignment. We did the bases are not always on the top and the bottom.

[00:53:28]Um, so you have to be just careful to um, they did put all the bases on the bottom. That was nice this time. Um, so parallel to the bases. So the bases are top and bottom. So parallel would be a cut this way. Um, if it had said perpendicular to the bases, we'd be cutting them vertically based on where the bases are. So a parallel cut for this would make a triangle.

[00:53:53]Parallel cut for this would make a circle.

[00:53:56]a rectangle or a square, a triangle, and a rectangle or a rectangle. So, it' be D and A makes a triangle.

[00:54:13]So, again, that little two-minute video for cross-sections is going to make you get all them cross-sections correct. Um, we're almost to the end. Okay, dilating again. So a dilation prism P is dilated by a scale factor of 0 to greater than zero and less than one. Okay, so prism A to B is getting smaller. So A to B is a reduction.

[00:54:42]Complete the sentences to compare the volume and surface area. The volume of prism A is blank than the volume of prism B.

[00:54:50]So if it's getting smaller, A is bigger.

[00:54:54]So the limit of a is is greater than is bigger than b. This is the smaller figure because we're reducing in size.

[00:55:01]And the surface area should also be everything is bigger if the figure is getting smaller. Everything is started off bigger. So they should both be greater than left.

[00:55:28]All right. So they give us some a picture. They tell us that this is a tangent to the circle. That's important that KL is a tangent means that this is a right angle. And now we can do Pyagorean theorem. So we can just pagorean theorem to solve this side.

[00:55:43]And then the perimeter is just the sum of the sides. So we have if we add these two together 9.6 and 5.4 that side's 15.

[00:55:54]9 and b. So I'll call it 9^2 + b^2 = 15.

[00:56:02]So solving that um 15^2 - 9^2 is 144 square rooted is 12. So um 12 would be the KL and the perimeter would be adding all the sides up. Perimeter is 9 12 and 15 added together 36.

[00:56:25]Okay. So the I'm not showing all the steps cuz hopefully in your math classes you in your math class you did do um thousands of pagan theorem problems it feels like. But um it really is algebra from here. You're just squaring these and then subtracting square.

[00:56:45]All right. And then for this one, back to trig. So several on trig one, two, so far we've had three at least three trig problems. So cosine from x. So they want to know from x which sides the adjacent over the hypotenuse.

[00:56:59]So this is just a matter of using the formula sheet and understanding from each angle what is what. Oops.

[00:57:07]Okay. This is from W. The tan is opposite over adjacent.

[00:57:15]Okay, so that one actually is pretty quick. It's just making sure you understand how to use the formula sheet and how to reference from each of the other each angle in the picture.

[00:57:27]Okay, Maria has a circular pizza diameter of 12.

[00:57:31]She cuts the pizza so that it has a central angle of 90.

[00:57:37]What's the what's the area of the slice?

[00:57:40]Okay, so we talked about on the on the formula sheet the area formula of a circle is p<unk> r^ squ.

[00:57:45]If you're trying to find the area of a slice of a circle, then you're going to do degree over 360 to figure out what percentage of the areas circle area that we want.

[00:57:59]Okay, so what's area?

[00:58:04]Doesn't tell us to put it in terms of pi. I wonder if they'll take um you know just like a also doesn't tell you what to round to.

[00:58:14]So that's why I'm thinking that they'll take um let me see the key says oh yeah it says 9 pi or it would take anything between 28 and okay so it does take since it doesn't tell you what to specify if you rounded it to whatever um was pretty close then they gave it to you. Okay. So the degree of a 90 the 90° cut was three 90° was the degree angle.

[00:58:37]So we're taking a quarter which is 9 over 90 over 360 is 1/2 uh 1/4. So a quarter of oops I forgot to put the six in of pi pi 6^ squ.

[00:58:51]Okay so again this is a quarter 90 over 360 is 1/4 if you simplify the fraction.

[00:58:57]And then 36 uh 62 is 36. So this is 9 pi if we rearrange it or 9 * pi is about 28 27. So they did they took 9 pi they also took 28.3 or 28.27.

[00:59:15]They took both all that.

[00:59:19]Um 9 pi is in terms of pi is the exact answer. So, okay, I'm at an hour. So, Karina draws a figure on the coordinate plane. She rotates the figure X or on the X axis. Okay, this is another one of those visuals. So, a lot of module 11, but they actually put a lot on these tests from last year that makes sure you understand the cross-sections and the revolutions. If you draw a um this one, if you draw any kind of rectangle, as long as it's not touching the x- axis, you'll be good. Um because if you were to draw this, it would create this like circle around this and it would look like this figure.

[01:00:05]I'm not really great with the visual drawings, so that video is super helpful.

[01:00:10]Okay, so the transformations uh transformation given or performed on a pentagon. This is a translation.

[01:00:17]I can tell because of the format of the rule. And this one says it's a rotation.

[01:00:22]Okay. So, pentagons are are congruent because um each transformation preserves side lengths which means the the lengths of the sides are the same. So all so it means congrent sides basically and then it preserves angle measures means congrent angles. So, because these are not including a dilation, the sides and angles stay the same.

[01:00:49]Um, let me see. I'm just curious how many people got that right. I feel like there was one probably more than half of the state. Yeah. Okay. It was 53% of the state got that right last year. That's good. Okay. Um, what is the question on this one? It's a proof.

[01:01:08]What could be reason for? Okay. So they give us a picture and they give us some statements. So they're giving us that these are marked and then they're telling us KG bisects FKJ.

[01:01:21]KG bisex FKJ that means that these two angles are congruent by the bis sector. So the step three should say angle F KH is congrent to H KJ.

[01:01:39]Okay, they don't ask us about that, but F KG H KJ.

[01:02:00]Okay, so this counts as these are the congruent sides and angles. So we have two angles and a side we know. So the choices are only between C and D really. Um then you want to look at the picture how it's marked and you can see that there are two angles and the side is between them. So you put an angle side angle.

[01:02:34]Joanna makes the claim if a polygon is a quadrilateral then pair two pairs of opposite sides are congruent. So this is the second counter example. They want to make sure you understand what a counter example is. So we still want it to be a quadrilateral but we don't want the opposite pair opposite sides to be congrent. They're congruent on A.

[01:02:51]They're congrent on C and B. So that this is just D because the opposite ones are not congruent here. I think a lot of people did not get that right.

[01:03:01]I think uh well 40% Let's know the counter example means to prove the second part of the statement to be wrong.

[01:03:13]A sequence of transformations select all that could be mapped. Okay, so they're congruent transformations. So that's the key.

[01:03:23]So reflection and a rotation are both congruence types. So A is good.

[01:03:29]A rotation and a reflection are congruent. So that's B is good.

[01:03:33]A dilation by a scale factor of three.

[01:03:35]That's going to make it not the same size.

[01:03:39]A dilation by a scale factor of third.

[01:03:41]It's going to change the size. A translation and a rotation are good. So this would be A, B, and E because it's making sure you understand that congruent things don't involve dilations.

[01:03:59]Okay. Complete the steps to describe a sequence of transformations that will map ABC onto itself.

[01:04:05]Okay, so it says step one, translate ABC up four units.

[01:04:11]So if we do that one, two, 3, 4, A, 2, 3, Okay, so we translate it up four units.

[01:04:22]It looks something like this.

[01:04:28]Step two, translate triangle.

[01:04:32]What? Translate triangle ABC down units down.

[01:04:41]If we want it to land on itself, it says it's a dilation here. We want a scale factor of one. Otherwise, it's going to change size. So, we just need to just do this so that it's four again to get it back down to where it need to be. So, we're just I don't know why we um So, you just move it back down. You moved it up. You moved it back down. And then just don't dilate it. Don't you don't actually dilate it. I mean, scale factor one means it didn't really move.

[01:05:13]Interesting question. Um I mean I think people 26% got it right but just because it was yeah that's my favorite question. Okay a figure shown complete the statement ABC the blank of ABC meet at point blank.

[01:05:35]Oh, okay. So, the medians are segments that connect the middle of a side to a vertex.

[01:05:48]The angle bis sectors are the ones that are cutting the angles in half.

[01:05:56]And the perpendicular bis sectors, you're going to see congruent segments and perpendicular cell. So there's no perpendicular symbols in the picture at all. There's no angle symbols either. So we're only only really choice is medians. And then um they meet at they're all meeting in the middle at point O.

[01:06:18]So A A and C.

[01:06:21]Well, A and O, but that's choice C.

[01:06:24]Okay. So that's it.