# Geometry 20 June 2014

Geometry 20 June 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Friday, June 20, 2014 — 1:15 to 4:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. Plane P is parallel to plane Q. If plane P is perpendicular to line ℓ, then plane Q

• (1) contains line ℓ
• (2) is parallel to line ℓ
• (3) is perpendicular to line ℓ
• (4) intersects, but is not perpendicular to line ℓ
Answer: (3) is perpendicular to line ℓ

2. In the diagram below, quadrilateral ABCD has vertices A(- 5,1), B(6,- 1), C(3,5), and D(- 2,7).

• (1) (1,3)
• (2) (1,3)
• (3) (1,4)
• (4) (2,3)
• (1) 6
• (2) 16
• (3) 24
• (4) 28

4. The measures of the angles of a triangle are in the ratio 2:3:4. In degrees, the measure of the largest angle of the triangle is

• (1) 20
• (2) 40
• (3) 80
• (4) 100

5. The diameter of the base of a right circular cylinder is 6 cm and  its height is 15 cm. In square centimeters, the lateral area of the cylinder is

• (1) 180π
• (2) 135π
• (3) 90π
• (4) 45π
Answer: (2) y + 2 = 2(x – 3)

6. When the system of equations y + 2x = x² and y = x is graphed on a set of axes, what is the total number of points of intersection?

• (1) 1
• (2) 2
• (3) 3
• (4) 0

7. The vertex angle of an isosceles triangle measures 15 degrees more than one of its base angles. How many degrees are there in a base angle of the triangle?

• (1) 50
• (2) 55
• (3) 65
• (4) 70

8. Circle O is graphed on the set of axes below. Which equation  represents circle O?

• (1) (x + 1)² + (y – 3)² = 9
• (2) (x – 1)² + (y + 3)² = 9
• (3) (x + 1)² + (y – 3)² = 6
• (4) (x – 1)² + (y + 3)² = 6
Answer: (1) (x + 1)² + (y – 3)² = 9

Which statement must always be true?

10. In the diagram below, ΔAEC ≅ ΔBED.

Which statement is not always true?

• (1) 2√2
• (2) 40
• (3) 2√10
• (4) 2√17

12. What are the truth values of the statement “Two is prime” and its negation?

• (1) The statement is false and its negation is true.
• (2) The statement is false and its negation is false.
• (3) The statement is true and its negation is true.
• (4) The statement is true and its negation is false.
Answer: (4) The statement is true and its negation is false.

13. A regular polygon has an exterior angle that measures 45°. How many sides does the polygon have?

• (1) 10
• (2) 8
• (3) 6
• (4) 4

• (1) 8
• (2) 16
• (3) √44
• (4) √136

15. If the surface area of a sphere is 144π square centimeters, what is the length of the diameter of the sphere, in centimeters?

• (1) 36
• (2) 18
• (3) 12
• (4) 6

16. Which numbers could represent the lengths of the sides of a triangle?

• (1) 5, 9, 14
• (2) 7, 7, 15
• (3) 1, 2, 4
• (4) 3, 6, 8

17. The equation of a line is 3y + 2x = 12. What is the slope of the line perpendicular to the given line?

• (1) 2/3
• (2) 3/2
• (3) – 2/3
• (4) – 3/2

18. In the diagram below, point K is in plane P

How many lines can be drawn through K, perpendicular to plane P ?

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

If m∠B = 123 and m∠D = 75, what is m∠C?

• (1) 57
• (2) 75
• (3) 105
• (4) 123
Answer: (2) y + 2 = 2(x – 3)

20. What is the equation of a line passing through the point (4,- 1) and parallel to the line whose equation is 2y – x = 8?

• (1) y = ½x – 3
• (2) y = ½x – 1
• (3) y = – 2x + 7
• (4) y = – 2x + 2
Answer: (1) y = ½x – 3

Geometry 20 June 2014 Questions Answers Keys

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