Geometry 12 August 2015 Questions Answer Keys

**The University of the State of New York**

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (Common Core)

Wednesday, August 12, 2015 — 8:30 to 11:30 a.m., only

Student Name:_________________________________________________________

School Name: _________________________________________________________

**1. A parallelogram must be a rectangle when its**

- (1) diagonals are perpendicular
- (2) diagonals are congruent
- (3) opposite sides are parallel
- (4) opposite sides are congruent

**2. If ΔA’B’C’ is the image of ΔABC, under which transformation will the triangles not be congruent?**

- (1) reflection over the x-axis
- (2) translation to the left 5 and down 4
- (3) dilation centered at the origin with scale factor 2
- (4) rotation of 270° counterclockwise about the origin

**3. If the rectangle below is continuously rotated about side w, which solid figure is formed?**

- (1) pyramid
- (2) rectangular prism
- (3) cone
- (4) cylinder

**4. Which expression is always equivalent to sin x when 0°< x <90°?**

- (1) cos (90° – x)
- (2) cos (45° – x)
- (3) cos (2x)
- (4) cos x

**5. In the diagram below, a square is graphed in the coordinate plane.**

A reflection over which line does not carry the square onto itself?

- (1) x = 5
- (2) y = 2
- (3) y = x
- (4) x + y = 4

**6. The image of ΔABC after a dilation of scale factor k centered at point A is ΔADE, as shown in the diagram below.**

Which statement is always true?

**7. A sequence of transformations maps rectangle ABCD onto rectangle A”B”C”D”, as shown in the diagram below**

Which sequence of transformations maps ABCD onto ABCD and then maps ABCD onto A’B’C’D’?

- (1) a reflection followed by a rotation
- (2) a reflection followed by a translation
- (3) a translation followed by a rotation
- (4) a translation followed by a reflection

If m∠R = 124°, what is m∠AFD?

- (1) 124°
- (2) 112°
- (3) 68°
- (4) 56°

**9. If x² + 4x + y² – 6y – 12 = 0 is the equation of a circle, the length of the radius is**

- (1) 25
- (2) 16
- (3) 5
- (4) 4

- (1) y = –
^{2}⁄_{3}x + 5 - (2) y = –
^{2}⁄_{3}x – 3 - (3) y =
^{3}⁄_{2}x + 7 - (4) y =
^{3}⁄_{2}x – 8

**11. Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region.**

To the nearest tenth of an inch, the largest possible length of a side of the square is

- (1) 3.5
- (2) 4.9
- (3) 5.0
- (4) 6.9

- (1) 6.4
- (2) 8
- (3) 12.5
- (4) 16

**13. In the diagram below, which single transformation was used to map triangle A onto triangle B?**

- (1) line reflection
- (2) rotation
- (3) dilation
- (4) translation

**14. In the diagram below, ΔDEF is the image of ΔABC after a clockwise rotation of 180º and a dilation where AB = 3, BC = 5.5, AC = 4.5, DE = 6, FD = 9, and EF = 11.**

Which relationship must always be true?

**15. In the diagram below, quadrilateral ABCD is inscribed in circle P.**

What is m∠ADC?

- (1) 70º
- (2) 72º
- (3) 108º
- (4) 110º

**16. A hemispherical tank is filled with water and has a diameter of 10 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?**

- (1) 16,336
- (2) 32,673
- (3) 130,690
- (4) 261,381

**17. In the diagram below, ΔABC ∼ΔADE.**

Which measurements are justified by this similarity?

- (1) AD = 3, AB = 6, AE = 4, and AC = 12
- (2) AD = 5, AB = 8, AE = 7, and AC = 10
- (3) AD = 3, AB = 9, AE = 5, and AC = 10
- (4) AD = 2, AB = 6, AE = 5, and AC = 15

What is the area of the sector formed by angle FOH?

- (1) 2π
- (2)
^{3}⁄_{2}π - (3) 6π
- (4) 24π

Given ΔAEC ∼ ΔBED, which equation is true?

**20. A triangle is dilated by a scale factor of 3 with the center of dilation at the origin. Which statement is true?**

- (1) The area of the image is nine times the area of the original triangle.
- (2) The perimeter of the image is nine times the perimeter of the original triangle.
- (3) The slope of any side of the image is three times the slope of the corresponding side of the original triangle.
- (4) The measure of each angle in the image is three times the measure of the corresponding angle of the original triangle.

**Geometry 12 August 2015 Questions Answers Keys**

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