Geometry 13 August 2013

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?

Answer: (2)

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

Answer: (1) 35

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

Answer: (1) One is not a prime number; true

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

Answer: (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

Answer: (4) (x + 5)² + (y – 4)² = 49

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

Answer: (2)

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

Answer: (3) 3

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

Answer: (4) right

Answer: (3)

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

Answer: (4) 65

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

Answer: (2) 12

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

Answer: (3) (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.

Answer: (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

Answer: (3) 10

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

Answer: (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

Answer: (2) lines y 5 and y -5

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

Answer: (3) 5:6

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”?