Geometry 26 January 2017 Questions Answer Keys

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

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (Common Core)

Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m., only

Student Name:_________________________________________________________

School Name: _________________________________________________________

**1. Which equation represents the line that passes through the point (2,2) and is parallel to y = ½x + 8?**

- (1) y= ½ x
- (2) y = -2x – 3
- (3) y = ½x + 3
- (4) y = – 2x + 3

Which statement must be true?

- (1) m∠BAC = m∠AED
- (2) m∠ABC = m∠ADE
- (3) m∠DAE = ½m∠BAC
- (4) m∠ACB = ½m∠DAB

**3. Given ΔABC ≅ ΔDEF, which statement is not always true?**

- (1)
- (2) m∠A = m∠D
- (3) area of
**Δ**ABC = area of**Δ**DEF - (4) perimeter of
**Δ**ABC = perimeter of**Δ**DEF

The perimeter of quadrilateral ADEF is equivalent to

- (1) AB + BC + AC
- (2) ½AB + ½AC
- (3) 2AB + 2AC
- (4) AB + AC

- (1) square
- (2) rhombus
- (3) rectangle
- (4) parallelogram

**6. Under which transformation would ΔA’B’C’, the image of ΔABC, not be congruent to ΔABC?**

- (1) reflection over the y-axis
- (2) rotation of 90º clockwise about the origin
- (3) translation of 3 units right and 2 units down
- (4) dilation with a scale factor of 2 centered at the origin

**7. The diagram below shows two similar triangles.**

- (1) 1.2
- (2) 5.6
- (3) 7.6
- (4) 8.8

**8. A farmer has 64 feet of fence to enclose a rectangular vegetable garden. Which dimensions would result in the biggest area for this garden?**

- (1) the length and the width are equal
- (2) the length is 2 more than the width
- (3) the length is 4 more than the width
- (4) the length is 6 more than the width

What is the perimeter of rectangle ABCD, to the nearest tenth?

- (1) 28.4
- (2) 32.8
- (3) 48.0
- (4) 62.4

**10. Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”, as shown below.**

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

**11. A solid metal prism has a rectangular base with sides of 4 inches and 6 inches, and a height of 4 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.**

What is the approximate volume of the remaining solid, in cubic inches?

- (1) 19
- (2) 77
- (3) 93
- (4) 96

**12. Given the right triangle in the diagram below, what is the value of x, to the nearest foot?**

- (1) 11
- (2) 17
- (3) 18
- (4) 22

- (1) B'(5,2) and C'(1,- 2)
- (2) B'(6,1) and C'(0,- 1)
- (3) B'(5,0) and C'(1,- 2)
- (4) B'(5,2) and C'(3,0)

- (1) 6
- (2) 22
- (3) 36
- (4) 48

**16. A parallelogram is always a rectangle if**

- (1) the diagonals are congruent
- (2) the diagonals bisect each other
- (3) the diagonals intersect at right angles
- (4) the opposite angles are congruent

**17. Which rotation about its center will carry a regular decagon onto itself?**

- (1) 54°
- (2) 162°
- (3) 198°
- (4) 252°

**18. The equation of a circle is x² + y² – 6y +1 = ****0. What are the coordinates of the center and the length of the radius of this circle?**

- (1) center (0,3) and radius = 2√2
- (2) center (0,3) and radius = 2√2
- (3) center (0,6) and radius = √35
- (4) center (0,6) and radius = √35

**19. Parallelogram ABCD has coordinates A(0,7) and C(2,1). Which statement would prove that ABCD is a rhombus?**

- (1) (5,1)
- (2) (5,0)
- (3) (6,- 1)
- (4) (6,0)

**Download Geometry 26 January 2017 Questions Answers Keys**

Geometry Examination Question |

Scoring Key and Rating Guide |

**See also: **