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
- (4) ∠AEF ≅ ∠ADF

**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

- (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)

**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) r
_{y=x} - (2) R
_{90°} - (3) T
_{0,-3} - (4) D
_{2}

**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

- (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.”

**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 r _{y-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)

**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

**Geometry 13 August 2015 Questions Answers Keys**

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