Geometry 13 August 2013 Questions Answer Keys

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (2005 Standard)

Tuesday, August 13, 2013 — 8:30 to 11:30 a.m., only

Student Name:_________________________________________________________

School Name: _________________________________________________________

Which statement can not always be proven?

- (1) 35
- (2) 55
- (3) 70
- (4) 110

**3. Given the statement: **

One is a prime number.

What is the negation and the truth value of the negation?

- (1) One is not a prime number; true
- (2) One is not a prime number; false
- (3) One is a composite number; true
- (4) One is a composite number; false

**4. Triangle ABC has the coordinates A(1,2), B(5,2), and C(5,5). Triangle ABC is rotated 180° about the origin to form triangle ABC. Triangle ABC is**

- (1) acute
- (2) isosceles
- (3) obtuse
- (4) right

**5. What is an equation of the circle with center (- 5,4) and a radius of 7?**

- (1) (x – 5)² + (y + 4)² = 14
- (2) (x – 5)² + (y + 4)² = 49
- (3) (x + 5)² + (y – 4)² = 14
- (4) (x + 5)² + (y – 4)² = 49

**6. In ΔABC, ∠A ≅ ∠B and ∠C is an obtuse angle. Which statement is true?**

- (1) 6
- (2) 2
- (3) 3
- (4) 9

- (1) straight
- (2) obtuse
- (3) acute
- (4) right

If m∠CAB = x + 40, m∠ACB = 3x + 10, and m∠CBD = 6x, what is m∠CAB?

- (1) 13
- (2) 25
- (3) 53
- (4) 65

- (1) 10
- (2) 12
- (3) 14
- (4) 16

**12. What is the equation of circle O shown in the diagram below?**

- (1) (x + 4)² + (y – 1)² = 3
- (2) (x – 4)² + (y + 1)² = 3
- (3) (x + 4)² + (y – 1)² = 9
- (4) (x – 4)² + (y + 1)² = 9

**13. The diagram below shows the construction of line m, parallel to line ℓ, through point P.**

Which theorem was used to justify this construction?

- (1) If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
- (2) If two lines are cut by a transversal and the interior angles on the same side are supplementary, the lines are parallel.
- (3) If two lines are perpendicular to the same line, they are parallel.
- (4) If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel.

**14. The lateral area of a right circular cone is equal to 120π cm². If the base of the cone has a diameter of 24 cm, what is the length of the slant height, in centimeters?**

- (1) 2.5
- (2) 5
- (3) 10
- (4) 15.7

**15. A student wrote the following equations:**

3y + 6 = 2x

2y – 3x = 6

The lines represented by these equations are

- (1) parallel
- (2) the same line
- (3) perpendicular
- (4) intersecting, but not perpendicular

**16. In a coordinate plane, the locus of points 5 units from the x-axis is the**

- (1) lines x 5 and x -5
- (2) lines y 5 and y -5
- (3) line x 5, only
- (4) line y 5, only

**17. The sides of a triangle are 8, 12, and 15. The longest side of a similar triangle is 18. What is the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle?**

- (1) 2:3
- (2) 4:9
- (3) 5:6
- (4) 25:36

**18. Lines m and n are in plane A. What is the converse of the statement “If lines m and n are parallel, then lines m and n do not intersect”?**

- (1) If lines m and n are not parallel, then lines m and n intersect.
- (2) If lines m and n are not parallel, then lines m and n do not intersect.
- (3) If lines m and n intersect, then lines m and n are not parallel.
- (4) If lines m and n do not intersect, then lines m and n are parallel.

**19. When the system of equations y + 2 = (x – 4)² and 2x + y – 6 =0 is solved graphically, the solution is**

- (1) (-4,-2) and (-2,2)
- (2) (4,-2) and (2,2)
- (3) (-4,2) and (-6,6)
- (4) (4,2) and (6,6)

- (1) 5
- (2) 13
- (3) 16
- (4) 32

**Geometry 13 August 2013 Questions Answers Keys**

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