Geometry Regents Exam - January 2023

Geometry Regents New York State Exam - January 2023

Geometry Regents New York State Exam Questions January 2023 (pdf)

Geometry Regents Exam January 2023 (Solutions 1 - 24)

Geometry Regents Exam January 2023 (Solutions 25 - 35)

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1. In the diagram below, a line reflection followed by a rotation maps △ABC onto △DEF.
2. A circle is continuously rotated about its diameter. Which three dimensional object will be formed?
3. In the diagram below of △CER
4. Right triangle ABC is shown below
5. In the diagram of △ABC below, AE bisects angle BAC, and altitude BD is drawn.
6. A jewelry company makes copper heart pendants. Each heart uses 0.75 in³ of copper and there is 0.323 pound of copper per cubic inch. If copper costs $3.68 per pound, what is the total cost for 24 copper hearts?
7. In right triangle LMN shown below, m∠M = 90°, MN = 12, and LM = 16.
8. In △ABC below, DE is drawn such that D and E are on AB and AC, respectively.
9. Which polygon does not always have congruent diagonals?
10. If the circumference of a standard lacrosse ball is 19.9 cm, what is the volume of this ball, to the nearest cubic centimeter?
11. Which polygon always has a minimum rotation of 180° about its center to carry it onto itself?
12. Circle O is drawn below with secant BCD. The length of tangent AD is 24.
13. The equation of a line is 3x - 5y = 8. All lines perpendicular to this line must have a slope of
14. In the diagram below of right triangle MDL, altitude DG is drawn to hypotenuse ML.
15. In parallelogram ABCD shown below, EB bisects ∠ABC
16. Segment AB is the perpendicular bisector of CD at point M. Which statement is always true?
17. In the diagram below of circle O, AC and BC are chords, and m∠ACB = 70°.
18. Quadrilateral BEST has diagonals that intersect at point D. Which statement would not be sufficient to prove quadrilateral BEST is a parallelogram?
19. The equation of line t is 3x - y = 6. Line m is the image of line t after a dilation with a scale factor of 1/2 centered at the origin. What is an equation of line m?
20. A cylindrical pool has a diameter of 16 feet and height of 4 feet. The pool is filled to 1/2 foot below the top. How much water does the pool contain, to the nearest gallon?
21. The area of △TAP is 36 cm². A second triangle, JOE, is formed by connecting the midpoints of each side of △TAP. What is the area of △JOE, in square centimeters?
22. On the set of axes below, the endpoints of AB have coordinates A(23,4) and B(5,2).
23. In the circle below, AD, AC, BC, and DC are chords, EDF is tangent at point D, and AD || BC.
24. In the diagram below of △ABC, D and E are the midpoints of AB and AC, respectively, and DE is drawn
25. Using a compass and straightedge, construct the angle bisector of ∠ABC.
26. On the set of axes below, △ABC and △DEF are graphed.
27. As shown in the diagram below, a symmetrical roof frame rises 4 feet above a house and has a width of 24 feet.
28. Directed line segment AB has endpoints whose coordinates are A(-2,5) and B(8,-1). Determine and state the coordinates of P, the point which divides the segment in the ratio 3:2.
29. In △ABC, AB = 5, AC = 12, and m∠A = 90°. In △DEF, m∠D = 90°, DF = 12, and EF = 13. Brett claims △ABC ≅ △DEF and △ABC ∼ △DEF. Is Brett correct? Explain why.
30. The volume of a triangular prism is 70 in³. The base of the prism is a right triangle with one leg whose measure is 5 inches. If the height of the prism is 4 inches, determine and state the length, in inches, of the other leg of the triangle.
31. Triangle ABC with coordinates A(-2,5), B(4,2), and C(-8,-1) is graphed on the set of axes below.
32. Sally and Mary both get ice cream from an ice cream truck. Sally’s ice cream is served as a cylinder with a diameter of 4 cm and a total height of 8 cm. Mary’s ice cream is served as a cone with a diameter of 7 cm and a total height of 12.5 cm. Assume that ice cream fills Sally’s cylinder and Mary’s cone.
33. The coordinates of the vertices of quadrilateral HYPE are H(-3,6), Y(2,9), P(8,-1), and E(3,-4). Prove HYPE is a rectangle.
34. Barry wants to find the height of a tree that is modeled in the diagram below, where ∠C is a right angle. The angle of elevation from point A on the ground to the top of the tree, H, is 40°. The angle of elevation from point B on the ground to the top of the tree, H, is 80°. The distance between points A and B is 85 feet.
35. Given: Triangle DUC with coordinates D(-3,-1), U(-1,8), and C(8,6)

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