1. In the diagram below, \triangle ABC \cong \triangle DEF.

Which sequence of transformations maps \triangle ABC onto \triangle DEF?

(1) a reflection over the x-axis followed by a translation
(2) a reflection over the y-axis followed by a translation
(3) a rotation of 180^{\circ} about the origin followed by a translation
(4) a counterclockwise rotation of 90^{\circ} about the origin followed by
a translation

2. On the set of axes below, the vertices of \triangle PQR have coordinates P(6,7), Q(2,1), and R(1,3).

What is the area of \triangle PQR?

(1) 10
(2) 20
(3) 25
(4) 50

3. In right triangle ABC, m\angle C = 90^{\circ}. If cos B = \dfrac{5}{13}, which function also equals \dfrac{5}{13}?

(1) tan A
(2) tan B
(3) sin A
(4) sin B

4. In the diagram below, m \widehat{ABC} = 268^{\circ}.

What is the number of degrees in the measure of \angle ABC?

(1) 134^{\circ}
(2) 92^{\circ}
(3) 68^{\circ}
(4) 46^{\circ}

5. Given \triangle MRO shown below, with trapezoid PTRO, MR = 9, MP = 2, and PO = 4.

What is the length of \overline{TR}?

(1) 4.5
(2) 5
(3) 3
(4) 6

6. A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

(1) The line segments are perpendicular, and the image is one-half of the length of the given line segment.
(2) The line segments are perpendicular, and the image is twice the length of the given line segment.
(3) The line segments are parallel, and the image is twice the length of the given line segment.
(4) The line segments are parallel, and the image is one-half of the length of the given line segment.

7. Which figure always has exactly four lines of reflection that map the figure onto itself?

(1) square
(2) rectangle
(3) regular octagon
(4) equilateral triangle

8. In the diagram below of circle O, chord \overline{DF} bisects chord \overline{BC} at E.

If BC = 12 and FE is 5 more than DE, then FE is

(1) 13
(2) 9
(3) 6
(4) 4

9. Kelly is completing a proof based on the figure below.

She was given that \angle A \cong \angle EDF, and has already proven \overline{AB} \cong \overline{DE}. Which pair of corresponding parts and triangle congruency method would not prove \triangle ABC \cong \triangle DEF?

(1) \overline{AC} \cong \overline{DF} and SAS
(2) \overline{BC} \cong \overline{EF} and SAS
(3) \angle C \cong \angle F and AAS
(4) \angle CBA \cong \angle FED and ASA

10. In the diagram below, \overline{DE} divides \overline{AB} and \overline{AC} proportionally, m\angle C = 26^{\circ}, m\angle A = 82^{\circ}, and \overline{DF} bisects \angle BDE.

The measure of angle DFB is

(1) 36^{\circ}
(2) 54^{\circ}
(3) 72^{\circ}
(4) 82^{\circ}

11. Which set of statements would describe a parallelogram that can always be classified as a rhombus?

I. Diagonals are perpendicular bisectors of each other.
II. Diagonals bisect the angles from which they are drawn.
III. Diagonals form four congruent isosceles right triangles.

(1) I and II
(2) I and III
(3) II and III
(4) I, II, and III

12. The equation of a circle is x^{2} + y^{2} - 12y + 20 = 0. What are the
coordinates of the center and the length of the radius of the circle?

(1) center (0,6) and radius 4
(2) center (0,-6) and radius 4
(3) center (0,6) and radius 16
(4) center (0,-6) and radius 16

13. In the diagram of \triangle RST below, m\angle T = 90^{\circ}, RS = 65, and ST = 60.

What is the measure of \angle S, to the nearest degree?

(1) 23^{\circ}
(2) 43^{\circ}
(3) 47^{\circ}
(4) 67^{\circ}

14. Triangle A'B'C' is the image of \triangle ABC after a dilation followed by a translation.
Which statement(s) would always be true with respect to this sequence of transformations?

I. \triangle ABC \cong \triangle A'B'C'
II. \triangle ABC \sim \triangle A'B'C'
III. \overline{AB} \| \overline{A'B'}
IV. AA' = BB'

(1) II, only
(2) I and II
(3) II and III
(4) II, III, and IV

15. Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on \overline{RW} such that RP:PW is 2:3. What are the coordinates of point P?

(1) (2,9)
(2) (0,11)
(3) (2,14)
(4) (10,2)

16. The pyramid shown below has a square base, a height of 7, and a volume of 84.

What is the length of the side of the base?

(1) 6
(2) 12
(3) 18
(4) 36

17. In the diagram below of triangle MNO, \angle M and \angle O are bisected by \overline{MS} and \overline{OR}, respectively. Segments MS and OR intersect at T, and m\angle N = 40^{\circ}.

If m\angle TMR = 28^{\circ}, the measure of angle OTS is

(1) 40^{\circ}
(2) 50^{\circ}
(3) 60^{\circ}
(4) 70^{\circ}

18. In the diagram below, right triangle ABC has legs whose lengths are
4 and 6.

What is the volume of the three-dimensional object formed by continuously rotating the right triangle around \overline{AB}?

(1) 32\pi
(2) 48\pi
(3) 96\pi
(4) 144\pi

19. What is an equation of a line that is perpendicular to the line whose equation is 2y = 3x - 10 and passes through (-6,1)?

(1) y = -\dfrac{2}{3}x - 5
(2) y = -\dfrac{2}{3}x - 3
(3) y = \dfrac{2}{3}x + 1
(4) y = \dfrac{2}{3}x + 10

20. In quadrilateral BLUE shown below, \overline{BE} \cong \overline{UL}.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?

(1) \overline{BL} \| \overline{EU}
(2) \overline{LU} \| \overline{BE}
(3) \overline{BE} \cong \overline{BL}
(4) \overline{LU} \cong \overline{EU}

21. A ladder 20 feet long leans against a building, forming an angle of 71^{\circ} with the level ground.
To the nearest foot, how high up the wall of the building does the ladder touch the building?

(1) 15
(2) 16
(3) 18
(4) 19

22. In the two distinct acute triangles ABC and DEF, \angle B \cong \angle E. Triangles ABC and DEF are congruent when there is a sequence of rigid motions that maps

(1) \angle A onto \angle D, and \angle C onto \angle F
(2) \overline{AC} onto \overline{DF}, and \overline{BC} onto \overline{EF}
(3) \angle C onto \angle F, and \overline{BC} onto \overline{EF}
(4) point A onto point D, and \overline{AB} onto \overline{DE}

23. A fabricator is hired to make a 27-foot-long solid metal railing for the stairs at the local library. The railing is modeled by the diagram below. The railing is 2.5 inches high and 2.5 inches wide and is comprised of a rectangular prism and a half-cylinder.

How much metal, to the nearest cubic inch, will the railing contain?

(1) 151
(2) 795
(3) 1808
(4) 2025

24. In the diagram below, AC = 7.2 and CE = 2.4.

Which statement is not sufficient to prove \triangle ABC \sim \triangle EDC?

(1) \overline{AB} \| \overline{ED}
(2) DE = 2.7 and AB = 8.1
(3) CD = 3.6 and BC = 10.8
(4) DE = 3.0, AB = 9.0, CD = 2.9, and BC = 8.7