# Geometry 16 June 2017

Geometry 16 June 2017 Questions Answer Keys

The University of the State of New York
The University Of The State Of New York
Regents High School Examination
Geometry
(Common Core)
Friday, June 16, 2017 — 9:15 a.m. to 12:15 p.m., only

Student Name:________________________________________________________

School Name:________________________________________________________

1. In the diagram below, ABC ≅ DEF.

Which sequence of transformations maps ABC onto DEF?

• (1) a reflection over the x-axis followed by a translation
• (2) a reflection over the y-axis followed by a translation
• (3) a rotation of 180° about the origin followed by a translation
• (4) a counterclockwise rotation of 90° about the origin followed by a translation

2. On the set of axes below, the vertices of PQR have coordinates P(6,7), Q(2,1), and R(1,3).

What is the area of PQR?

• (1) 10
• (2) 20
• (3) 25
• (4) 50

3. In right triangle ABC, m∠C 90°. If cos B = 5/13, which function also equals  5/13?

• (1) tan A
• (2) tan
• (3) sin A
• (4) sin B

4. In the diagram below, mABC 268°.

What is the number of degrees in the measure of ∠ABC?

• (1) 134°
• (2) 92°
• (3) 68°
• (4) 46°

5. Given ΔMRO shown below, with trapezoid PTRO, MR = 9,
MP = 2, and PO = 4.

What is the length of TR?

• (1) 4.5
• (2) 5
• (3) 3
• (4) 6

6. A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

• (1) The line segments are perpendicular, and the image is one-half of the length of the given line segment.
• (2) The line segments are perpendicular, and the image is twice the length of the given line segment.
• (3) The line segments are parallel, and the image is twice the length of the given line segment.
• (4) The line segments are parallel, and the image is one-half of the length of the given line segment.
Answer: (3) The line segments are parallel, and the image is twice the length of the given line segment.

7. Which figure always has exactly four lines of reflection that map the figure onto itself?

• (1) square
• (2) rectangle
• (3) regular octagon
• (4) equilateral triangle

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8. In the diagram below of circle O, chord DF bisects chord BC at E.

If BC = 12 and FE is 5 more than DE, then FE is

• (1) 13
• (2) 9
• (3) 6
• (4) 4

11. Which set of statements would describe a parallelogram that can always be classified as a rhombus?

I. Diagonals are perpendicular bisectors of each other.
II. Diagonals bisect the angles from which they are drawn.
III. Diagonals form four congruent isosceles right triangles.

• (1) I and II
• (2) I and III
• (3) II and III
• (4) I, II, and III
Answer: (4) I, II, and III

12. The equation of a circle is x2 + y2 – 12y + 20 = 0. What are the coordinates of the center and the length of the radius of the circle?

• (1) center (0,6) and radius 4
• (2) center (0, –6) and radius 4
• (3) center (0,6) and radius 16
• (4) center (0, –6) and radius 16

16 . The pyramid shown below has a square base, a height of 7, and a volume of 84.

What is the length of the side of the base?

• (1) 6
• (2) 12
• (3) 18
• (4) 36