Geometry Regents Exam - August 2023

Geometry Regents New York State Exam - August 2023

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

Geometry Regents Exam August 2023 (Solutions 1 - 24)

Geometry Regents Exam August 2023 (Solutions 25 - 35)

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1. A plane intersects a sphere. Which two-dimensional shape is formed by this cross section?
2. The endpoints of AB are A(-5,3) and B(7,-5). Point P is on AB such that AP:PB 5 3:1. What are the coordinates of point P?
3. Zach placed the foot of an extension ladder 8 feet from the base of the house and extended the ladder 25 feet to reach the house. To the nearest degree, what is the measure of the angle the ladder makes with the ground?
4. Darnell models a cup with the cylinder below. He measured the diameter of the cup to be 10 cm and the height to be 9 cm. If Darnell fills the cup with water to a height of 8 cm, what is the volume of the water in the cup, to the nearest cubic centimeter?
5. Which quadrilateral has diagonals that are always perpendicular?
6. Which regular polygon would carry onto itself after a rotation of 300° about its center?
7. The rectangle drawn below is continuously rotated about side S. Which three-dimensional figure is formed by this rotation?
8. An equation of the line perpendicular to the line whose equation is 4x - 5y = 6 and passes through the point (-2,3) is
9. In circle P below, diameter AC and radius BP are drawn such that m∠APB = 110°.
10. In △ABC, side BC is extended through C to D. If m∠A = 30° and m∠ACD = 110°, what is the longest side of △ABC?
11. Right triangle ACT has m∠A = 90°. Which expression is always equivalent to cos T?
12. A regular pyramid with a square base is made of solid glass. It has a base area of 36 cm² and a height of 10 cm. If the density of glass is 2.7 grams per cubic centimeter, the mass of the pyramid, in grams, is
13. The equation of a circle is x² + y² + 12x = -27. What are the coordinates of the center and the length of the radius of the circle?
14. In triangle ABC below, D is a point on AB and E is a point on AC, such that DE || BC
15. In the diagram below, point E is located inside square ABCD such that ∠ABE is equilateral, and CE is drawn.
16. In the diagram below of quadrilateral ADBE, DE is the perpendicular bisector of AB
17. What is the image of (4,3) after a reflection over the line y = 1?
18. In the diagram below, a cone has a diameter of 16 inches and a slant height of 17 inches. What is the volume of the cone, in cubic inches?
19. In the diagram below, lines ℓ and m intersect lines n and p to create the shaded quadrilateral as shown.
20. In the circle below, secants TSR and TMH intersect at T, SR = 5, HM = 9, TM = 3, and TS = x. Which equation could be used to find the value of x?
21. On the set of axes below, the coordinates of three vertices of trapezoid ABCD are A(2,1), B(5,4), and D(-2,3). Which point could be vertex C?
22. In the diagram below, △ABC ≅ nDEC.
23. If △TAP is dilated by a scale factor of 0.5, which statement about the image, △T’A’P’, is true?
24. In the diagram below of △ABC, X and Y are points on AB and AC, respectively, such that m∠AYX = m∠B.
25. On the set of axes below, congruent quadrilaterals ROCK and R’O’C’K’ are graphed. Describe a sequence of transformations that would map quadrilateral ROCK onto quadrilateral R’O’C’K'.
26. In triangle CEM, CE = 3x + 10, ME = 5x - 14, and CM = 2x - 6. Determine and state the value of x that would make △CEM an isosceles triangle with the vertex angle at E.
27. A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end of the shadow to the top of the flagpole. Determine and state, to the nearest tenth of a foot, the height of the flagpole.
28. A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the tabletops?
29. Using a compass and straightedge, construct a midsegment of △AHL below.
30. Right triangle STR is shown below, with m∠T 5 90°. Altitude TQ is drawn to SQR, and TQ = 8. If the ratio SQ:QR is 1:4, determine and state the length of SR.
31. Line AB is dilated by a scale factor of 2 centered at point A. Evan thinks that the dilation of AB will result in a line parallel to AB, not passing through points A or B. Nathan thinks that the dilation of AB will result in the same line, AB. Who is correct? Explain why.
32. Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height of 1.5 feet. The concrete walls of the fire pit are going to be 9 inches thick. If a bag of concrete mix will fill 0.6 ft³, determine and state the minimum number of bags needed to build the fire pit
33. A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below. Two conditions for proper support are:

• The beam reaches the telephone pole at 70% of the telephone pole’s height above the ground.
• The beam forms a 65° angle with the ground. Determine and state, to the nearest tenth of a meter, the length of the support beam that meets these conditions for this telephone pole. Determine and state, to the nearest tenth of a meter, how far the support beam must be placed from the base of the pole to meet the conditions.

34. The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,-1). Prove that ABCD is a parallelogram, but not a rectangle.
35. In the diagram below of quadrilateral FACT

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