# Geometry 13 August 2015

Geometry 13 August 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Thursday, August 13, 2015 — 8:30 to 11:30 a.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

Which statement must be true?

• (1) ∠ACF ≅ ∠BCF
• (2) ∠DAE ≅ ∠DFE
• (3) ∠BCD ≅ ∠ABD

2. In a circle whose equation is (x – 1)² + (y + 3)² = 9, the coordinates of the center and length of its radius are

• (1) (1, – 3) and r = 81
• (2) (- 1,3) and r = 81
• (3) (1, – 3) and r = 3
• (4) (- 1,3) and r = 3
Answer: (3) (1, – 3) and r = 3
• (1) 106
• (2) 115
• (3) 130
• (4) 156

4. What are the coordinates of P, the image of point P(x,y) after translation T4,4?

• (1) (x – 4,y – 4)
• (2) (x + 4,y + 4)
• (3) (4x, 4y)
• (4) (4,4)
Answer: (2) (x + 4,y + 4)

5. The statement “x > 5 or x < 3” is false when x is equal to

• (1) 1
• (2) 2
• (3) 7
• (4) 4

6. Triangle JTM is shown on the graph below.

Which transformation would result in an image that is not congruent to ΔJTM?

• (1) ry=x
• (2) R90°
• (3) T0,-3
• (4) D2

8. Which pair of edges is not coplanar in the cube shown below?

9. What is an equation of the line that passes through the point (- 2,1) and is parallel to the line whose equation is 4x – 2y = 8?

• (1) y = ½ x + 2
• (2) y = ½ x – 2
• (3) y = 2x + 5
• (4) y = 2x – 5
Answer: (3) y = 2x + 5
• (1) 61
• (2) 64
• (3) 116
• (4) 122

11. The corresponding medians of two similar triangles are 8 and 20. If the perimeter of the larger triangle is 45, what is the perimeter of the smaller triangle?

• (1) 14
• (2) 18
• (3) 33
• (4) 37

12. Which construction of parallel lines is justified by the theorem “If two lines are cut by a transversal to form congruent alternate interior angles, then the lines are parallel”?

13. Given: “If a polygon is a triangle, then the sum of its interior angles is 180°.”

What is the contrapositive of this statement?

• (1) “If the sum of the interior angles of a polygon is not 180°, then it is not a triangle.”
• (2) “A polygon is a triangle if and only if the sum of its interior angles is 180°.”
• (3) “If a polygon is not a triangle, then the sum of the interior angles is not 180°.”
• (4) “If the sum of the interior angles of a polygon is 180°, then it is a triangle.”
Answer: (1) “If the sum of the interior angles of a polygon is not 180°, then it is not a triangle.”

14. In the diagram below, point P is not on line ℓ.

How many distinct planes that contain point P are also perpendicular to line ℓ?

• (1) 1
• (2) 2
• (3) 0
• (4) an infinite amount

15. The image of ΔABC after the transformation ry-axis  is ΔA’B’C’.

Which property is not preserved?

• (1) distance
• (2) orientation
• (3) collinearity
• (4) angle measure

16. The equations y = 2x + 3 and y = – x² -x + 1 are graphed on the same set of axes. The coordinates of a point in the solution of this system of equations are

• (1) (0,1)
• (2) (1,5)
• (3) ( – 1, – 2)
• (4) ( – 2, – 1)
Answer: (4) ( – 2, – 1)

17. Which quadrilateral has diagonals that are always perpendicular bisectors of each other?

• (1) square
• (2) rectangle
• (3) trapezoid
• (4) parallelogram
• (1) 40
• (2) 70
• (3) 110
• (4) 140

19. In parallelogram JKLM, m∠L exceeds m∠M by 30 degrees. What is the measure of ∠J?

• (1) 75°
• (2) 105°
• (3) 165°
• (4) 195°

20. Which equation represents the circle shown in the graph below?

• (1) (x – 5)² (y + 3)² = 1
• (2) (x + 5)² (y – 3)² = 1
• (3) (x – 5)² (y + 3)² = 2
• (4) (x + 5)² (y – 3)² = 2
Answer: (2) (x + 5)² (y – 3)² = 1

Geometry 13 August 2015 Questions Answers Keys

 Geometry Examination Question Scoring Key and Rating Guide