Geometry Regents 2

1. Based on the diagram below, which statement is true?

(a) a $\parallel$ b

(b) a $\parallel$ c

(d) d $\parallel$ e

Question 1 of 30

2. Which transformation produces a figure similar but not congruent to the original figure?

(a) translation

(b) rotation

(d) reflection

Question 2 of 30

3. In isosceles triangle ABC, AB = BC. Which statement will always be true?

(a) m < A = m < B

(b) m < A > m < B

(d) m < A = m < C

Question 3 of 30

4. If $\bigtriangleup$ ABC ~ $\bigtriangleup$ DEF, m < A = 40, and m < B = 60, what is m < F?

(a) 80

(b) 60

(d) 20

Question 4 of 30

5. What is the converse of the statement, "If Steve is late, then Mary gets promoted"?

(a) If Mary gets promoted, then Steve is late.

(b) Steve is late if and only if Mary gets promoted.

(d) If Mary does not get promoted, then Steve isn't late.

Question 5 of 30

6. In the diagram below of trapezoid ABCD, $\overline{AB}\parallel\overline{CD}$ , F is the midpoint of $\overline{AD}$ , and G is the midpoint of $\overline{BC}$ .
If AB = 15 and FG = 22, what is the length of $\overline{CD}$ ?

(a) 24

(b) 29

(c) 32

(d) 37

Question 6 of 30

7. In the diagram below of parallelogram ABCD with diagonals $\overline{AC}$ and $\overline{BD}$ , m < 1 = 80 and m < BCD = 65.

What is the measure of < 2?
(a) 25
(b) 35
(c) 45
(d) 55

Question 7 of 30

8. Line segment AB is tangent to circle O at point A. What type of triangle is always formed when points A, B and O are connected?
(a) right
(b) isosceles
(c) scalene
(d) equilateral

Question 8 of 30

9. What is the sum of all interior angles of a pentagon?
(a) $360^{\circ}$
(b) $480^{\circ}$
(c) $540^{\circ}$
(d) $720^{\circ}$

Question 9 of 30

10. What is the length of the line segment with endpoints A(3,-1) and B(6,5)?
(a) 3
(b) 5
(c) 5 $\sqrt{3}$
(d) 3 $\sqrt{5}$

Question 10 of 30

11. What is the image of the point (3,-6) after a $90^o$ rotation?
(a) (3,-6)
(b) (-3,-6)
(c) (6, 3)
(d) (-6, -3)

Question 11 of 30

12. In a coordinate plane, how many points are both 6 units from the origin and 5 units from the y-axis?
(a) 1
(b) 2
(c) 3
(d) 4

Question 12 of 30

13. In the diagram below of circle O, diameter $\overline{AOB}$ is perpendicular to chord $\overline{CD}$ at point E, $\overline{OB}$ = 6, and $\overline{OE}$ = 2. What is the length of $\overline{CE}$ ?
(a) 4 $\sqrt{3}$
(b) 2 $\sqrt{3}$
(c) 8 $\sqrt{2}$
(d) 4 $\sqrt{2}$

Question 13 of 30

14. In the diagram below, $\overline{BD}$ bisects < ABC and < A [latex]\cong[/latex] < C.

What method could be used to prove $\bigtriangleup$ ABD $\cong$ $\bigtriangleup$ BCD?
(a) AAA
(b) SSS
(c) AAS
(d) SAS

Question 14 of 30

15. What type of quadrilateral has diagonals that always bisect each other and also bisect its angles?
(a) rectangle
(b) rhombus
(c) trapezoid
(d) parallelogram

Question 15 of 30

16. The equation of a circle is $x^2 + (y - 4)^2$ = 9. What are the center and radius of the circle?
(a) center = (0,4); radius = 3
(b) center = (0,4); radius = 9
(c) center = (0,-4); radius = 3
(d) center = (0,-4); radius = 9

Question 16 of 30

17. Which transformation can map the letter S onto itself?
(a) line reflection
(b) translation
(c) rotation
(d) glide reflection

Question 17 of 30

18. What is the slope of a line perpendicular to the line whose equation is y = 5x - 4?
(a) 5
(b) -5
(c) - $\frac{1}{5}$
(d) $\frac{1}{5}$

Question 18 of 30

19. If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral could be a
(a) square
(b) rectangle
(c) trapezoid
(d) rhombus

Question 19 of 30

20. Mr. Peterson wants to place a sprinkler in his yard so that it is 20 feet from the sidewalk, s, and also 10 feet from the pole, P. As shown in the diagram below, the pole is 25 feet away from the sidewalk.

How many locations are possible for the sprinkler?
(a) 1
(b) 2
(c) 3
(d) 0

Question 20 of 30

21. Triangle ABC has angles in the ratio of 2:3:5. What type of triangle is $\bigtriangleup$ ABC?
(a) isosceles
(b) acute
(c) obtuse
(d) right

Question 21 of 30

22. point P is on line f. What is the total number of planes that are perpendicular to line f and also pass through point P?
(a) 1
(b) 2
(c) 4
(d) infinite

Question 22 of 30

23. What is the negation of the statement "Squares are rectangles"?
(a) Rectangles are squares.
(b) Rectangles are not squares.
(c) It is not the case that squares are rectangles.
(d) It is not the case that rectangles are squares.

Question 23 of 30

24. A right circular cylinder has a volume of 3,000 cubic inches and a height of 12 inches. What is the radius of the cylinder to the nearest tenth of an inch?
(a) 8.9
(b) 19.8
(c) 26.3
(d) 79.6

Question 24 of 30

25. Which equation represents a line parallel to the line whose equation is 4y + 3x = 10?
(a) 4y + 5x = 12
(b) 8y + 6x = 12
(c) 4y - 5x = 12
(d) 8y - 6x = 12

Question 25 of 30

26. Isosceles triagle ABCD has diagonals $\overline{AC}$ and $\overline{BD}$ . If AC = 4x + 5 and BD = 6x - 3, what is the value of x?
(a) $\frac{3}{2}$
(b) 2
(c) 3
(d) 4

Question 26 of 30

27. In the diagram below, circle A and circle B are shown. What is the total number of lines of tangency that are common to circle A and circle B?
(a) 1
(b) 2
(c) 3
(d) 4

Question 27 of 30

28. Triangle ABC has vertices A(2,3), B(1,1), and C(5,0). Under translation A', the image point of A, is located at (5,2). Under the same translation, point C' is located at
(a) (0,4)
(b) (4,0)
(c) (8,-1)
(d) (-1,8)

Question 28 of 30

29. Two triangles are similar, and the ratio of each pair of corresponding sides is 3:1. Which statement regarding the two triangles is true?
(a) Their perimeters have a ratio of 6:1.
(b) Their altitudes have a ratio of 3:1.
(c) Their corresponding angles have a ratio of 3:1.
(d) Their areas have a ratio of 3:1.

Question 29 of 30

30. In the triangle below, points D, E, and F are midpoints. Given AB = 20, BC = 24, and AC = 32, what is the perimeter of triangle DEF?
(a) 38
(b) 42
(c) 58
(d) 76

Question 30 of 30