2025 Florida Geometry EOC Released Test Questions #31-45

Added: 2026-05-14

[00:00:00]Welcome to my third and final video in my series covering questions from the 2025 Florida Geometry EOCC release test.

[00:00:08]This video covers questions 31 to 45. As always, I recommend that you download the test and try the questions out first yourself before watching the video. All right, here we go. Number 31.

[00:00:22]Quadrilateral ABCD is inscribed in circle F as shown. Complete the statements to describe the measure in degrees of angle ADC. So down here it says angle ABC and angle A DC are what?

[00:00:35]Complimentary, congruent or supplementary. And we notice that these two angles are opposite each other. And what we need to remember about inscribed quadrilaterals is that opposite angles are supplementary.

[00:00:49]And knowing that we could use the fact that angle ABC is 82 degrees to subtract from 180 to find that the measure of angle ABC is 98°.

[00:01:02]Number 32. A circle with two tangent segments is shown. This question has two parts. Part A, which equation is true?

[00:01:10]So what we need to remember here is that when we have two tangent segments that are tangent to the same circle and share a common end point like f then those two tangent segments are congruent. So we can use that to write the following equation.

[00:01:25]4x - 10 = 2x. So the answer to part a is a.

[00:01:34]And now we could use that equation to solve for x. So, we're going to subtract 4x from both sides here.

[00:01:47]That gives us -10 = -2x.

[00:01:52]Then we're going to go ahead and divide both sides by -2.

[00:01:59]And that gives us x= 5. So, the answer for part B is 5.

[00:02:06]Number 33. A right triangle is shown with side lengths in units. Select an expression to complete the trig ratio for the triangle. And down here it says the tangent of the 30° angle is 7 radical 41 over which one of these options.

[00:02:24]You should always make sure that you remember SOA when you're dealing with trig ratios. This stands for s is opposite over hypotenuse. Cosine is adjacent over hypotenuse. And tangent is opposite over adjacent. That's what we're using here. So we see that the leg opposite the 30° angle is 7 radical 41.

[00:02:47]That's why it's on top down here. But we need the adjacent leg and we don't have it. So how can we find that? What we can do is we can recognize that this triangle is a 30 60 90 triangle and that the three sides of a 30 60 90 triangle have a special relationship. That relationship is as follows. The shorter leg is n and the hypotenuse is always double the length of the shorter leg. So 2 n and the longer leg is n radical 3. So down here we can see that n in this particular triangle is the same as 7 radical 41. And we can use that to substitute for this n here.

[00:03:32]So we're going to write this instead of n we're going to write 7 radical 41* radical 3.

[00:03:41]Now remember you can just multiply 41 * 3 because they're both radicals. and we get 7 radical 123.

[00:03:51]And that is our answer. C number 34. Select all the figures that have a triangular cross-section when sliced parallel to their bases. So the very simple thing to remember here is that whenever slicing a pyramid, prism, cone or cylinder parallel to the base that the cross-section is always going to have the shape of the base itself. So if we slice here parallel to the base of this triangular prism, then the cross-section is going to be a triangle.

[00:04:24]If we slice here parallel to the base of this cone, the cross-section is going to be a circle. If we slice here parallel to the base of this cube, the cross-section is going to be a square.

[00:04:35]If we slice parallel to the base of this rectangular pyramid, the cross-section is going to be a rectangle. And if we slice parallel to the base of this triangular pyramid, the cross-section is going to be a triangle. So our two answers are A and D.

[00:04:53]Number 35. Prism A is dilated by a scale factor greater than zero and less than one to create prism B. Complete the sentences to compare the volume and surface area of the two prisms. So a very simple concept to remember here is whenever we multiply by a number greater than one then our product our answer is going to be larger than the original number. But whenever we multiply by a fraction or a decimal, a number in between 0 and 1, then our product, our answer is going to be a number that is smaller than the original number. And that's what we're doing here. The scale factor is greater than zero but less than one. So it's a fraction or a decimal. Now the volume and the surface area are going to change in the same way. If the dimensions get smaller, then the volume and the surface area will also get smaller. So let's take a look at this one here. The volume of prism A is going to be what? Well, prism A is the original, right? So prism B is smaller. So it's going to be greater than the volume of prism B. And the surface area of prism A, once again, prism A is larger than prism B is also going to be greater than the surface area of prism B.

[00:06:12]Number 36. Line segments JK, KL, and LJ form a triangle JKL as shown with dimensions and units. Segment KL is tangent to the circle. Segment LJ is a seeant of the circle. And segment JK is a diameter of the circle. What is the perimeter in units of triangle JKL? So, we already know the length of this side here is 9. We don't know the length of LK. And we can find the length of LJ very easily by simply adding 9.6 + 5.4 and that's going to be 15. So how do we find the length of LK? In order to do that we need to remember the relationship between a tangent segment and a seeant that have a common endpoint. And the relationship is this.

[00:07:03]the tangent segment squared is equal to the external part of the seeant times the length of the entire seecant. So if we call LK X, we just put a variable X here, we could write the following equation again. The tangent segment squared, so X^2 equals the exterior part of the seeant 9.6 6 times the entire length of the seeant which is 15.

[00:07:40]So now we can work this out. 9.6 * 15 is 144. And now we need to take the square root of both sides and we get x = 12. So now we know the length of lk. So all we got to do now is add 15 + 12 + 9 and that is 36.

[00:08:11]So that's our answer.

[00:08:13]Number 37. Triangle WXY is shown with side lengths and units. Match each trig ratio to its value. So here we're looking for the cosine of X and the tangent of W.

[00:08:25]Remember to always call upon sookoa to help you with your trig ratios. So is s is opposite over hypotenuse. K cosine is adjacent over hypotenuse. And toa tangent is opposite over adjacent. And remember that the opposite leg is the leg that does not touch the angle that is not part of the angle. So when we're looking for the cosine of x, here's x and cosine is adjacent over hypotenuse.

[00:08:55]So the leg that is adjacent to angle x is xy which measures 15 and then the hypotenuse is opposite the right angle and that's 17. So the cosine of x is 15 over 17.

[00:09:11]Now for the tangent of w, remember tangent is the only ratio that does not involve the hypotenuse. Here is W. Here tangent is opposite over adjacent. The leg that is not part of angle W is XY which is 15.

[00:09:27]And then the adjacent leg is WY which is 8. So the tangent of W is L 15 over 8.

[00:09:37]Number 38. Maria has a circular pizza with a diameter of 12 in. She cuts the pizza so that each slice has a central angle that measures 90°. What is the area in square inches of each slice of pizza? So, I always recommend on problems like this, drawing a diagram of the problem. It doesn't need to be perfect. You can see my circle's not perfect here, but it's going to give us the idea. Now, Maria cuts this pizza into slices that have each of them a central angle that measures 90 degrees.

[00:10:09]So that's going to look kind of like this.

[00:10:16]And what we can recognize is that if this was a perfect circle that Maria basically cut this pizza into four equal slices. So if we find the area of the entire pizza and divide by four, that's going to give us the area of each slice.

[00:10:32]So we can see that the pizza has a diameter of 12 in. But remember, when doing area of a circle, we don't want to use diameter. We want to use radius. So that's going to be a radius here of six.

[00:10:44]So we're going to use the formula for area of a circle, which is area is p<unk> r^ 2. And we're going to leave pi as a symbol. So we're just going to deal with r. So we're going to substitute these numbers here. So this is pi * 6^ 2, which is 36 pi. Now, that's the area of the entire pizza. We want the area of each slice. So, all we're going to do is divide by four, and that gives us 9 pi. So, the area of each slice is 9 pi.

[00:11:19]Number 39. Karina draws a figure on the coordinate plane. Then, she rotates the figure around the x-axis. The resulting object is shown. Use the connect line tool to create a possible figure that Karina could have drawn. So, we see that the three-dimensional figure is a cylinder. And we should know by now that the two-dimensional object that we rotate around the line to create a cylinder is a rectangle. What we have to note is that there's a hollowed out cylindrical tunnel on the inside. So, this is empty space. So, now how do we put this on the coordinate plane? Very simple. We're going to draw a rectangle, but in order to account for this hollowed out space, we're going to leave a space, a gap between the rectangle and the x-axis.

[00:12:03]So that could look something like this.

[00:12:11]So you can see when this rectangle rotates around x, this space here will result in this empty space here.

[00:12:19]Number 40. The transformations given are performed on pentagon a b cde e to create pentagon a prime b prime c prime d prime e prime x comma y becomes x - 5 y - 6 and a counterclockwise rotation of 37° about the origin. Complete the sentence to explain whether or not the pentagons are congruent. So this first transformation is a translation.

[00:12:46]X - 5 means the figure is moving five steps to the left and Y minus 6 means the figure is moving six steps down. And then we also have this counterclockwise rotation. Both of these are rigid motions.

[00:13:04]Rigid motions preserve side length and angle measure. So when you perform rigid motions, the resulting image is congruent to the original. the image is congruent to the pre-image. Remember that the only transformation that does not result in a congruent figure is a dilation.

[00:13:25]So now we can go ahead and complete the sentence. Pentagons ABCDE and A prime B prime C prime D prime E prime are or are not congruent. Well, they are because both transformations are rigid motions because each neither only the first only the second. know each transformation preserves side lengths and angle measures.

[00:13:50]Number 41. A figure is shown. Segment KG bisects angle FKJ. Angles GFK and JHK are congruent.

[00:13:59]Line segments FK and HK are congruent. A partial proof is shown. What could be reason number four? So notice that we're missing statement three, but they want us to find reason four. So let's go ahead and see what we have here. Let's take a look at our givens. First FK is congruent to HK. They have that marked right here. And angle GFK is congruent to angle JHK. They have that marked right here. Then next they say KG bisects FKJ. So let's take a look at that. KG is this line right here and it bisects this angle F KJ. So what does that mean? When you bisect something, you cut it in half, right? That means that this angle here is congruent to this angle here. So down here in three we can write angle FKH is congruent to angle HKJ and that's by definition of angle bis sector. So now we look we have here angle side angle angle side angle. So what could be reason four? Why do we know that these two triangles are congruent? Because of angle side angle congruence.

[00:15:16]Number 42. Joanna makes the following claim. If a polygon is a quadrilateral, then two pairs of opposite sides are congruent. Which polygon is a counter example to Joanna's claim? So remember that a counter example is an example that proves a claim to be false. So let's see if we could find it here. If we look at A, opposite sides are congruent. So this is not our counter example. And B, the same opposite sides are congruent. How about C? C could be confusing. It could trick you because in C all four sides are congruent. But think about it. If all four sides are congruent, then technically opposite sides are congruent. So C is not the answer. The counter example is here.

[00:15:59]This is D. This is a kite. And in a kite, opposite sides aren't congruent.

[00:16:04]consecutive sides are congruent. So this is our counter example number 43. A sequence of transformations maps triangle QRS onto congruent triangle XYZ. Select all the sequences of transformations that could have mapped triangle QRS onto triangle XYZ.

[00:16:24]So when we talk about mapping a triangle or mapping any figure onto another, that means that one figure will basically cover the other figure. They'll line up perfectly and that can only happen if the figures are congruent. Now we've already discussed this, right? There are four transformations and there is only one transformation that is not a rigid transformation. The only transformation that does not maintain congruence is a dilation.

[00:16:56]Now, a dilation could maintain congruence if you're multiplying by a scale factor of one or negative 1, but any other scale factor and you do not have a congruent figure. So, if you look at a, a reflection across the x-axis followed by a 90°ree clockwise rotation about the origin, there's no dilation here. This would work. B. A 180°ree clockwise rotation about the origin followed by a reflection across the line y equals 3.

[00:17:28]This would also work because there's no dilation here. C. A dilation by a scale factor of three. We could stop right there. A dilation by a scale factor of three. That figure is not going to be congruent. D. A reflection across the line y equals x followed by a dilation by a scale factor of 1/3. Nope. This figure is not going to be congruent. E.

[00:17:51]A translation one unit left and three units up followed by a 270°ree counterclockwise rotation about the origin. Yes, there's no dilation here.

[00:18:01]This figure will be congruent.

[00:18:06]44. Triangle ABC is shown on the coordinate grid. Complete the steps to describe a sequence of transformations that will map triangle ABC onto itself.

[00:18:17]So remember when we talk about mapping one figure onto another, that means that the one figure will line up perfectly with the other one. So if we talk about mapping triangle ABC onto itself, that means after we do whatever transformations we're going to do to it, it's going to end up right here where it is originally. So let's go ahead and take a look at these steps. Step one says translate triangle ABC four units up. So let's do that. 1 2 3 4 1 2 3 4 and 1 2 3 4.

[00:18:56]And so this is where our triangle is after being translated four units up.

[00:19:01]Now step two says translate triangle ABC blank units down. So, if we want to eventually map right back onto the original and we went up four units, then it makes sense that we would go down four units. And that would put this triangle right back where it started.

[00:19:28]But we're not done. And this might be the confusing part because I've told you that dilations are not rigid motions and then when you perform a dilation that the object you end up with is not congruent because you're either shrinking or enlarging the object. But there's actually one case where multiplying by a certain scale factor does not shrink or enlarge an object.

[00:19:55]That would be multiplying by negative 1 or positive one because whenever you multiply by one, the numbers don't change, right? Anything times one equals itself. Now, multiplying by a scale factor of negative 1 does result in a 180° rotation.

[00:20:13]So, the scale factor that we're going to use here to keep this triangle where it is is a scale factor of one.

[00:20:22]45. A figure is shown. Complete the statement to describe triangle ABC. So we're looking here. Let's take a look.

[00:20:29]The medians, angle bis sectors, or perpendicular bis sectors of triangle ABC meet at point C, D, or O. So we're looking here at these three lines. So BF, AE, and CD. And we're trying to figure out are they medians, angle bis sectors, or perpendicular bis sectors?

[00:20:47]Well, let's go backwards. uh they're not perpendicular bis sectors because there's no indication that these are right angles. We don't know that. So we can't call them perpendicular bis sectors for sure. They're not angle bis sectors because there's no indication that these angles are congruent. So we can't call them that. We can call them medians. They are medians. What is a median? A median is a line segment that goes from an angle to the midpoint of the opposite side. And we can see here that FA and FC are congruent. So F is a midpoint. We can see here that A D and DB are congruent. So D is a midpoint. And we can see here that CE and EB are congruent. So E is a midpoint. Therefore, the medians of triangle ABC meet at what point? They meet right here at point O.

[00:21:44]All right. So, this is the end of my third video in this series reviewing the 2025 Florida Geometry EOCC release test.

[00:21:51]I hope that you have found these videos helpful. Good luck.