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

**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

**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

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.

**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

**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

**Geometry 20 June 2014 Questions Answers Keys**

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