This exam was adminstered in June 2025.
More Regents problems.
June 2025 Geometry Regents
*Part I *
Each correct answer will receive 2 credits. No partial credit.
*1. The perimeter of a triangle is 18. What is the perimeter of a similar triangle after a dilation with a scale factor of 3?
(1) 6 (2) 18 (3) 54 (4) 162
**Answer: (3) 54 **
The perimeter of a dilated triangle is the perimeter of the original times the scale factor, so 18 times 3 equals 54, which is Choice (3).
It is not the scale factor squared – that would be the area, which has two dimensions being expanded.
*2. The Washington Monument, shown below, is in Washington, D.C. At a point on the ground 200 feet from the center of the base of the monument, the angle of elevation to the top of the monument is 70.19°. *
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*What is the height of the monument, to the nearest foot?
(1) 188 (2) 213 (3) 555 (4) 590
**Answer: (3) 555 **
If you’ve ever been there, then you might know that it is 555 feet tall, and they did NOT change this fact for this problem. If you didn’t know that, you can calculate it using the tangent ratio, because you have the angle and the adjacent side and you are looking for the opposite side.
tan 70.19 = x / 200 x = 200 tan 70.19 = 555.217...,
which is about 555, which is Choice (3).
*3. On the set of axes below, △EQA and △SUL are graphed. *
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- Which sequence of transformations shows that △EQA ≅ △SUL?
(1) Rotate △EQA 90° counterclockwise about the origin and then translate 9 units right and 1 unit down. (2) Rotate △EQA 90° counterclockwise about the origin and then reflect over the line x = 4. (3) Reflect △EQA over the x-axis and then rotate 90° clockwise about the origin. (4) Translate △EQA 10 units right and then reflect over the line x = -1.
**Answer: (1) Rotate △EQA 90° counterclockwise about the origin and then translate 9 units right and 1 unit down. **
Make sure you are going the correct direction: you want to go from the top left to the bottom right. There are multiple methods of getting there, so check the choices one by one.
In Choice (1), EQA goes to Quadrant III with E’(-5,-2), Q(-1,-2), A’(-1,-5), which is facing the same direction as SUL. A transformation of T9,-1 brings AEQ to SUL. This is the correct answer.
In Choice (2), EQA goes to Quadrant III with E’(-5,-2), Q(-1,-2), A’(-1,-5), which is facing the same direction as SUL. A reflection would change the orientation and would not map onto SUL. Eliminate Choice (2).
In Choice (3), EQA goes to Quadrant I but changes its orientation. When E’Q’A’ is rotated 90 degrees, it will not map ontol SUL because the orientations are different. Eliminate Choice (3).