Geometry Regents 1

1. Line segment AB is shown in the diagram below.

Which two segments of construction marks, labeled I, II, III, and IV, is the perpendicular bisector of line segment AB?

(a) I and II

(b) I and III

(d) III and IV

Question 1 of 30

2. In the diagram of $\bigtriangleup$ ABC below, $\overline{AB}\cong\overline{AC}$ . The measure of < C is $35^{\circ}$ .

What is the measure of < A?

(a) $35^{\circ}$

(b) $70^{\circ}$

(c) $95^{\circ}$

(d) $110^{\circ}$

Question 2 of 30

3. What is the negation of the statement, "I am not going to ride my bike"?
(a) I like riding my bike.
(b) I am going to ride my bike.
(c) I ride my bike, then I like my bike.
(d) If I don't like my bike, then I won't ride my bike.

Question 3 of 30

4. Which statement is true about all parallelograms?
(a) All four sides are congruent.
(b) Two pairs of sides are congruent.
(c) Adjacent angles are complementary.
(d) Interior angles are congruent.

Question 4 of 30

5. In $\bigtriangleup$ ABC, m < A = x, m < B = 3x + 2, and m < C = 5x - 11. What is the value of x?
(a) 21
(b) 23
(c) 25
(d) 27

Question 5 of 30

6. Describe the transformation shown in the diagram below.
(a) Translation
(b) Dilation
(c) Rotation
(d) Reflection

Question 6 of 30

7. The angles of triangle ABC ire in the ratio of 9:4:5. What is the measure of the largest angle?
(a) $70^{\circ}$
(b) $80^{\circ}$
(c) $90^{\circ}$
(d) $100^{\circ}$

Question 7 of 30

8. What is the equation of a circle with a radius of 4 and a center at (-2,3)?
(a) $(x + 2)^2 + (y - 3)^2$ = 4
(b) $(x - 2)^2 + (y + 3)^2$ = 4
(c) $(x + 2)^2 + (y - 3)^2$ = 16
(d) $(x - 2)^2 + (y + 3)^2$ = 16

Question 8 of 30

9. In $\bigtriangleup$ ABC, AB = 7, BC = 9, AC = 12. List the angles of $\bigtriangleup$ ABC in order from smallest to largest.
(a) < A, < B, < C
(b) < C, < A, < B
(c) < B, < A, < C
(d) < C, < B, < A

Question 9 of 30

10. In the diagram below of rhomubus ABCD, m < C = 70.
What is m < ABD?
(a) 35
(b) 55
(c) 70
(d) 110

Question 10 of 30

11. Cities A and B are 18 miles apart. How many points are 10 miles from city A and 12 miles from city B?
(a) 0
(b) 1
(c) 2
(d) 3

Question 11 of 30

12. The volume, in cubic centimeters, of a sphere whose radius is 3 centimeters is
(a) 6 $\pi$
(b) 9 $\pi$
(c) 24 $\pi$
(d) 36 $\pi$

Question 12 of 30

13. A transformation that always preserves both length and orientation is
(a) Translation
(b) Dilation
(c) Line Reflection
(d) Glide Reflection

Question 13 of 30

14. What polygon does the sum of the measures of all the interior angles equal the sum of the measures of exterior angles?
(a) Quadrilateral
(b) Triangle
(c) Pentagon
(d) Hexagon

Question 14 of 30

15. In the diagram of $\bigtriangleup$ ABC below, D is the midpoint of $\overline{AB}$ , E is the midpoint of $\overline{BC}$ , and F is the midpoint of $\overline{AC}$ .
If AB = 24, BC = 16, and AC = 20, what is the perimeter of trapezoid ABEF?
(a) 42
(b) 48
(c) 64
(d) 60

Question 15 of 30

16. Which equation represents a line parallel to the line whose equation is 4y - 8x = 14?
(a) 5y + 12x = 12
(b) 5y - 12x = 8
(c) 2y + 4x = 6
(d) 2y - 4x = 10

Question 16 of 30

17. In the diagram of circle O below, chords $\overline{AB}$ and $\overline{CD}$ intersect at E.
If AE = 3, EB = 12, and CE = 4, what is the length of $\overline{ED}$ ?
(a) 6
(b) 9
(c) 11
(d) 15

Question 17 of 30

18. In the diagram of circle O below, chords $\overline{AB}$ and $\overline{CD}$ intersect at E, such that the measure of arc AC = $64^{\circ}$ and the measure of arc DB = $52^{\circ}$ .
What is the measure of < AEC?
(a) 52
(b) 58
(c) 64
(d) 70

Question 18 of 30

19. The point (2,-4) is rotated $180^{\circ}$ about the origin then dilated by a scale factor of 3. What are the coordinates of the resulting image?
(a) (-6,12)
(b) (6,-12)
(c) (6,12)
(d) (-6,-12)

Question 19 of 30

20. The surface area of a sphere is 36 $\pi$ , what is the volume?
(a) 24 $\pi$
(b) 32 $\pi$
(c) 36 $\pi$
(d) 48 $\pi$

Question 20 of 30

21. If a line segment has endpoints A(4x + 9,5y) and B(2x - 1,-y), what are the coordinates of the midpoint of $\overline{AB}$ ?
(a) (3x + 4,2y)
(b) (6x + 8,4y)
(c) (3x + 6,2y)
(d) (6x - 8,4y)

Question 21 of 30

22. What is the slope of a line perpendicular to the line whose equation is 2y = -8x + 6?
(a) -8
(b) $\frac{1}{8}$
(c) -4
(d) $\frac{1}{4}$

Question 22 of 30

23. How many points are both 5 units away from the origin and also 2 units away from the line y = 3?
(a) 1
(b) 2
(c) 3
(d) 4

Question 23 of 30

24. What is the measure of each interior angle of a regular octagon?
(a) $120^{\circ}$
(b) $135^{\circ}$
(c) $145^{\circ}$
(d) $160^{\circ}$

Question 24 of 30

25. In the diagram of $\bigtriangleup$ ABC below, m < A = [latex]45^{\circ}[/latex], m < B = [latex]80^{\circ}[/latex], and $\overline{AC}$ is extended through D.

What is the measure of < BCD?
(a) $55^{\circ}$
(b) $80^{\circ}$
(c) $100^{\circ}$
(d) $125^{\circ}$

Question 25 of 30

26. Point A is located at (2,-5). The point is reflected across the x-axis. Its image is located at
(a) (2,5)
(b) (-2,5)
(c) (-2,-5)
(d) (-5,2)

Question 26 of 30

27. In an equilateral triangle, what is the difference between the sum of the exterior angles and the sum of the interior angles?
(a) $60^{\circ}$
(b) $90^{\circ}$
(c) $120^{\circ}$
(d) $180^{\circ}$

Question 27 of 30

28. Given the system of equations:
y = $x^2$ - 4x
x = 2
The number of points of intersection is:
(a) 0
(b) 1
(c) 2
(d) 3

Question 28 of 30

29. If two different lines are perpendicular to the same plane, they are
(a) collinear
(b) congruent
(c) coplanar
(d) consecutive

Question 29 of 30

30. How many common tangent lines can be drawn to the two tangent circles shown below?
(a) 1
(b) 2
(c) 3
(d) 4

Question 30 of 30