Florida Geometry EOC Released Test Questions #16-30

Added: 2026-05-11

[00:00:00]All right, welcome to my second video covering the 2025 Florida Geometry EOC released test. This video covers questions 16 to 30. As always, I recommend that you download the released test and try the questions yourself first before watching the video. All right, here we go.

[00:00:19]Number 16. A two-dimensional figure and a vertical line are shown. The figure is rotated about the vertical line. Which object could be the result of this rotation? So, rotated about the vertical line means it's going to go around this vertical line and we need to imagine what the three-dimensional figure is going to look like. So, this top part here is flat and it's going to go around and it's going to make a circular top.

[00:00:46]And then the bottom is going to dip in.

[00:00:48]Now, if the bottom was a straight line like this, if this was a triangle, then what we'd end up with is a cone. But, it's not a straight line. It has a bit of a curve to it. So, it's going to be A.

[00:01:05]Number 17. Which figure shows steps leading to the construction of a perpendicular bisector? Well, it's not A because A is an angle bisector. It's C and let me explain why. To find the perpendicular bisector, we want to find the midpoint, right, which is the halfway mark between two endpoints, and we also want to draw a line through that midpoint that is perpendicular to the other line. And the way we do that is we open the compass so that we can get an arc that goes more than halfway between the two points, and then we draw that same arc from each endpoint. And so, where those two endpoints intersect, not only marks the midpoint of the line, but it is also perpendicular to the line.

[00:01:54]Number 18. A figure and a vertical line are shown. Which object is generated by rotating the figure around the vertical line? So, this is the same as the last rotation we did. The only difference here is notice that the figure is not connected to the vertical line. So, there's going to be a space in the middle that is going to be empty. It's going to be a hollow space in the middle there. So, it's got to be either B or D, correct? Now, if we look at the outside here, it's curved, not angled. So, it has to be D.

[00:02:30]Number 19, triangle M has a base length of 18 in and a height of 12 in.

[00:02:36]Triangle N is congruent to triangle M. What is the area in square inches of triangle N? So, if triangle N is congruent to triangle M, that [clears throat] means they are exactly the same size and shape. So, whatever area triangle M has, that's going to be the same area as triangle N.

[00:02:56]All we have to do now is remember the formula for area of a triangle and we can say area of a triangle is half base times height. Or another way that we can write that is area of a triangle is base times height divided by two. So, if we do 18 times 12 divided by two, we can do 18 divided by two first if we want and we end up with 9 times 12 which is 108. And that's our answer.

[00:03:29]Number 20, the equation of a circle is given. X minus 1 squared plus Y plus 4 squared equals 12.25.

[00:03:37]Which graph represents the equation?

[00:03:40]So, a quick glance at these four graphs and we can see that these circles are all the same size, but they're in different locations. So, what we need to do is figure out what the center of of circle is so we can figure out which circle is in the right location. In order to do that, we need to remember the format of the equation of a circle, and it looks like this.

[00:04:00]X minus H squared plus Y minus K squared equals R squared, where H is the X value of the center, and K is the Y value of the center. Now, normally, when if we had the circle and we needed to write the equation, then I would tell my students to do this, to put parentheses.

[00:04:24]So, we have X minus and a parenthesis for H squared plus Y minus and a parenthesis for K squared equals R squared, yes? And so, where did this -1 come from? Well, that negative's already there, so that -1 came from our X value is a positive one.

[00:04:46]And where did this positive four come from? Well, there's a negative here, so if I have a negative, how do I get a positive four? If I also put a negative four in here.

[00:04:56]So, we can see that our center is located at the point one {comma} -4. Now, you can get there easier once you understand this concept just by taking the opposite of these numbers. The opposite of -1 is positive one, and the opposite of positive four is -4. So, the graph that shows the circle at the correct location is graph A.

[00:05:21]1, -4.

[00:05:25]Number 21. A circle with chord AB and its perpendicular bisector CD is shown.

[00:05:31]The measure of arc AC is 28°. What is the measure in degrees of arc BD?

[00:05:37]So, they tell us here that CD is a perpendicular bisector of chord AB. Now, chord AB intercepts arc AB. So, since CD is a diameter and it bisects chord AB, it also bisects arc AB. So, if arc AC is 28°, then arc CB is also 28°.

[00:06:02]Now, they want us to find the measure in degrees of arc BD.

[00:06:06]But, if we think of arc CD, right? We can see that arc CD is intercepted by a diameter, which makes this a semicircle, which makes the measure of the arc 180°.

[00:06:18]So, then what is going to be the measure of BD? It's going to be 180 minus this 28, which is 152.

[00:06:31]So, the measure in degrees of arc BD is 100 52°.

[00:06:38]Number 22. Triangle XYZ is transformed to create triangle X'Y'Z' using the rule (x, y) becomes (x + b, y + c). So, we could stop there and realize that we're adding something to x and adding something to y. So, this is a translation.

[00:06:57]All right, let's move on. Triangle XYZ has the vertices (3, -2), (3, -4), and (0, -4) respectively. That means this point is x, this is y, this is z.

[00:07:08]Triangle X'Y'Z' has the vertices (-1, 5), (-1, 3), and (-4, 3) respectively. Again, X', Y', Z'.

[00:07:20]What are the values of b and c? So, if we look at b, b is simply what do we add to the x values in the first triangle to get the x values in the second triangle?

[00:07:32]And c is what do we add to the y values in the first triangle to end up with the y values in the second triangle? So, if we take a look at the X values of the first point, how do we get from three to -1? Well, we add -4. So, that is B. B is -4. Now, if we look at the Y values, how do we get from -2 to 5? Well, we add 7.

[00:07:59]So, C is 7.

[00:08:02]Number 23.

[00:08:04]A tile is in the shape of an isosceles trapezoid. The tile is divided into two parts by its midsegment. The trapezoid with lengths in centimeters is shown.

[00:08:12]The top part is shaded. What is the area in square centimeters of the shaded part? All right. So, we first need to remember the formula for area of a trapezoid, which is area equals half times the height times B1 + B2. And so, B1 and B2 are the two bases. The two bases are the two parallel sides. So, we're not finding the area of the entire trapezoid, just the top shaded part. So, we have one base is 6. We need the other base, and we need the height. Now, this line here is a midsegment, which means it is halfway between the two bases. So, if the height of the entire trapezoid is 4 cm, that means the height of the shaded part is 2 cm. Now, for the length of this other base. This is the midsegment. What do we need to remember about midsegments? The midsegment is half the sum of base one and base two. So, if I add these two bases together and divide by two, then that's going to give me the length of the midsegment. So, 6 + 12 is 18, and 18 / 2 is 9. So, that is the length of this base. So, now we're going to go ahead and go into our formula here and plug in these numbers.

[00:09:36]So, we have half times our height, which is two times six plus nine.

[00:09:46]Now, half of two is one and six plus nine is 15, and one times 15 is 15. So, our answer is B.

[00:09:57]Number 24, an isosceles trapezoid is shown. What is the measure of angle HIJ in degrees? So, we see we have two angles marked with something. This angle K here is X and angle I is 2X + 6. So, in order to do this, we need to remember the special properties of an isosceles trapezoid, particularity of opposite angles, and opposite angles are supplementary. That means they add together to make 180. So, we can go ahead and write this equation here.

[00:10:31]2X + 6 + X = 180.

[00:10:38]So, then we're going to combine like terms here. We end up with 3X + 6 = 180.

[00:10:44]Then, we are going to subtract six from both sides and we get 3X = 174.

[00:10:56]And then, we divide both sides by three and we get X = 58.

[00:11:07]So, now we're going to take that 58 and plug it in here. So, two times 58 + 6. 2 * 58 is 116 and 116 + 6 is 122.

[00:11:25]So, HIJ measures 122.

[00:11:30]Number 25, rectangle G has a length of 15 in and a width of 20 in. What is the Rectangle H is similar to rectangle G and has a length of 18 ft. What is the width in feet of rectangle H? All right, so I always recommend drawing a diagram of the problem because sometimes we can understand it better when we can see it.

[00:11:49]So here are my two rectangles. This is going to be rectangle G, which measures 15 in by 20 in, and this is going to be rectangle H, which measures 18 ft by X ft cuz we don't know this width yet.

[00:12:07]And we need to remember that similar figures, corresponding sides are proportional. So we can use a proportion to find the missing width of rectangle H. So we start by writing a ratio of the length to the width of rectangle G. So that's going to be 15 over 20. And we can simplify. We can divide both of these parts by five. That gives us 3/4.

[00:12:32]And now we can use this 3/4 to write a proportion. So we're going to write 3/4 equals blank over blank, and then this 18 has to go in here. Now this 3/4 is length over width. So we have to do the same thing, length over width. So we're going to put the 18 here and the X here. Now we can cross multiply and solve the equation. So 3 * X is 3X and 4 * 18 is 72.

[00:12:59]And then when we divide both sides by three, we get X equals 24.

[00:13:08]But sometimes you can just kind of see the relationship between the numbers by looking at it. So we can see here that 3 * 6 is 18. So we know that with fractions, whatever you multiply the top by, you have to also multiply the bottom by. So down here we would do 4 * 6, which is, once again, 24.

[00:13:29]So, the width in feet of rectangle H is 24 ft.

[00:13:36]Number 26, transversal line KP passes through parallel lines JM and RS as shown. Complete the sentences to describe angle QHJ.

[00:13:46]So, it says here, angles PQR and QHJ are what? Congruent, supplementary, or complementary? Well, let's take a look at them. So, here is PQR and measures 32°.

[00:13:57]And here is QHJ. Now, let's take a look at their properties. So, PQR is to the left of the transversal and it is under its parallel line.

[00:14:09]Same applies to QHJ.

[00:14:11]QHJ is also to the left of the transversal and under its parallel line. So, both of these angles are in the same position.

[00:14:22]That makes them corresponding angles, and corresponding angles are congruent. So, now we can go ahead and complete this. Angles PQR and QHJ are congruent because they are corresponding angles.

[00:14:38]So, the measure of angle QHJ is the same as the measure of angle PQR, and that is 32°.

[00:14:48]Number 27, trapezoid ABCD is shown.

[00:14:52]Select all the true statements. So, what do we see here? If we take a look at this side, AD, notice how AX and XB are both marked with two bars, that means they're congruent. That makes X what? A midpoint.

[00:15:06]And if we look here at side BC, we see the same thing. BY and YC are both marked with one bar, that means Y is also a midpoint. That makes XY a mid-segment.

[00:15:24]And the mid-segment of a trapezoid has two properties. The first property is that it is parallel to the two bases.

[00:15:33]So, we see that XY here is parallel to CD.

[00:15:41]And we also know that the measure of the mid-segment is equal to half the sum of the measure of the two bases. So, if I add AB and CD together and then divide by two or multiply by half, that's going to give me the measure of XY and that's what it says here for D. XY equals half AB + CD.

[00:16:08]Number 28. A regular pentagonal pyramid is shown with units in centimeters. The slant height is 11 cm, the apothem of the base is 4 cm, and the side length of the base is 6 cm. Which expression represents the surface area in square centimeters of the pyramid? So, we're going to have to find the area of the base and then the lateral area. So, let's go ahead and do one at a time.

[00:16:30]Let's do the area of the base first. We have to use apothem. So, remember that formula looks like this, half times the apothem times the measure of one side times the number of sides. So, if we write that out with the actual numbers, that's going to be half times four times six times five cuz we have to multiply there are five sides that measure six.

[00:16:56]Okay? Now, the lateral area is going to be half times the base, which is the same thing as a side. The base of one triangle is a side. So, we're going to put here base.

[00:17:08]And again we're going to multiply that we're going to do that five times cuz there's five triangles. So, we're going to put number of sides here as well times the slant height.

[00:17:18]If we plug those numbers in, it's going to look like this. Half times six times five times 11.

[00:17:28]Now, remember that when you multiply, you can multiply in any order you want.

[00:17:32]So, I'm going to rearrange this first part to look like this.

[00:17:37]Half times six times five times four.

[00:17:44]I'm going to keep the second part the same.

[00:17:49]And now we notice that for both pieces of this, it starts with half times six times five.

[00:17:54]Well, what is half times six times five?

[00:17:56]It's 15.

[00:17:58]So, if I rewrite this as 15 times four, plus again, half times six times five is 15 times 11, we can actually write this a different way using distributive property. We could write this as 15 times 4 + 11. Now, that's not down here, but all we have to do is remember where this 15 came from. It came from half times six times five.

[00:18:27]And another way to write half times six times five is to write six times five divided by two times 4 + 11, and the answer is D.

[00:18:40]Number 29. Ashley draws a map of her town on a coordinate grid where each unit represents 1 mile. A pizza shop in the town delivers to any location within a 6-mile radius. Ashley's house is located at point 9,3. The pizza shop is located at point 6,7. Complete the sentences to describe whether Ashley's house is within the delivery radius of the pizza shop. So, it says the shortest distance from the pizza shop to Ashley's house is blank miles. So, what we have to do here is distance formula. So, remember distance formula is the square root of x2 - x1 squared plus y2 - y1 squared. Now, remember, this is not as difficult as it seems. All you're doing is taking the difference between the x's and squaring it and the difference between the y's and squaring it and then adding them together and taking the square root. So, here, what's the difference between 9 and 6? It's 3, so that's going to be 3 squared.

[00:19:54]Plus, what's the difference between 3 and 7? It's 4 or you want to call it -4, doesn't really matter.

[00:20:02]So, we're going to do that squared. So, then what is 3 squared? It's 9.

[00:20:10]And what is -4 squared? It's 16.

[00:20:15]And 9 + 16 is 25 and the square root of 25 is 5.

[00:20:25]So, the shortest distance from the pizza shop to Ashley's house is 5 miles. Therefore, Ashley's house is within the delivery radius of the pizza shop.

[00:20:41]All right, number 30 is a very easy problem. Let's take a look. Kyla claims that the sum of the interior angles of any closed figure is 360° or greater.

[00:20:52]Use the connect line tool to draw a figure that is a counterexample to Kyla's claim. So, a counterexample is an example that proves a claim to be false. So, if we could think of a figure whose interior angles, the sum of the interior angles is less than 360, then that can be our counterexample. And hopefully, we all know that the sum of the interior angles of any triangle is 180. So, all we would have to do here is drag and drop three points anywhere onto this graph and connect them together to draw our triangle, and that is our counterexample.

[00:21:35]All right, I hope that you found this video helpful. Stay tuned for the third and final video in the series where I will cover questions 31 to 45.

[00:21:44]Good luck.