1. Geometry EOCT
In the figure below, the diagonals of the parallelogram ABCD intersect at (5,2). What are the coordinates of C?
(7,3)
(8,3)
(9,4)
(10,4)

2. Geometry EOCT
2. If line CD intersects with segment AB at K and line CD is the perpendicular bisector of segment AB, which statement must be true?
CK = KD
AB = CD
AC = BC
AC = AD

3. Geometry EOCT
3. Planes P and R are parallel, and line m is in plane R. Which of the following statements is true?
Every line that is perpendicular to m intersects plane P.
Every line in plane P is parallel to m.
No line in plane P is skew to m.
No line in plane P intersects line m.

4. Geometry EOCT
4. In the figure below, p is parallel to q. Which of the following are corresponding angles?
<1 and <2
<1 and <3
<2 and <3
<3 and <4

5. Geometry EOCT
5. On segment PQ, R is between P and Q. X does not lie on segment PQ and segment XR is not perpendicular to segment PQ. Which of the following describes <XRQ and <XRP?
Complementary angles
Congruent angles
Supplementary angles
Vertical angles

6. Geometry EOCT
6. A toy company produces a new toy called a “Zerk.” All Zerks are either pink or green. Which of these is NOT necessarily true?
If an object is blue, it is not a Zerk.
If a Zerk is not pink, it must be green.
If an object is pink or green, it must be a Zerk.
If an object is not pink or green, it cannot be a Zerk.

7. Geometry EOCT
7. Which of these statements is the best conclusion for the following list of statements?
<A and <B are acute angles in triangle ABC
<A and <B are base and vertex angles respectively
Triangle ABC is an equilateral triangle
m<A = m<B C. m<A + m<B = 900
<A and <B are D. m<A > m<B complementary

8. Geometry EOCT
8. In the xy-plane, if the lines y=6 and y=2x + k intersect at (1,6), what is the value of k? 1 3 4 6

9. Geometry EOCT
9. After reviewing the diagrams below, Jessie came to the conclusion that every angle within a triangle must be less than or equal to 90 degrees.
Which triangle below serves as a counterexample of Jessie’s argument?
A. B.
C. D.

10. Geometry EOCT 10. What is the converse of the following statement?
If Gerald swims, he will wear his red swimsuit.
If Gerald wears his red swimsuit, then he swims.
If Gerald does not swim, then he will not wear his red swimsuit.
If Gerald does not wear his red swimsuit, then he will not swim.
If Gerald swims, then he will wear his blue swimsuit.

11. Geometry EOCT
11. In the figure below, line p is parallel to line m. If RS=ST, m<RYX=90 degrees, what is the measure of <RXY?
300
450
600
900

12. Geometry EOCT 12. Which statement about a parallelogram must be true?
All of its sides are congruent.
Its diagonals are congruent.
Its opposite angles are congruent.
At least one angle is a right angle.

13. Geometry EOCT 13. The following triangles are similar. What is DE? 6/5
8/5
9/5 2

14. Geometry EOCT
14. Four points lie in a plane so that no three of them lie on a line. If lines are drawn connecting all pairs of these points, how many such lines are there? 4 6 8 12

15. Geometry EOCT
15. An open area at a local high school is in the shape of a quadrilateral. Two sidewalks crisscross this open area as diagonals of a quadrilateral. If the walkways cross at their midpoints and the walkways are equal in length, what is the shape of the open area?
a parallelogram
a rhombus
a rectangle
a trapezoid

16. Geometry EOCT
16. C is the circumcenter of triangle DEF. C is on triangle DEF. If DE = 6 and DF = 8, find the radius of the circle. 4 5 6 3

17. Geometry EOCT
17. For triangle ABC and triangle ARQ, AB=AR and m<C=m<Q. If AB:BC is 4:7 and AB = 10, find RQ.
A. 7/4
B. 13
C. 17.5
D. 16

18. Geometry EOCT
18. In the figure below, to prove that segment MN is parallel to segment AC, which of the following statements must be true?
MN = ½ AC
Their slopes are equal
MA=MB
AM= ½ CN

19. Geometry EOCT
19. Which equation best describes the line containing points A(-5,4) and B(1,2)?
x – 3y = -5
x + 3y = -5
x + 3y = 7
3x + y = 5

20. Geometry EOCT
20. Which set of information is NOT enough to prove that triangle ABC is congruent to triangle DEF?
m<A=m<D, m<C=m<F, BC=EF
AB=DE, BC=EF, m<B=m<E
m<A=m<D, m<C=m<F, AC=DF
m<A=m<D, AC=DF, BC=EF

21. Geometry EOCT
21. Which statement will ALWAYS provide a counterexample to the statement below?
If two angles are congruent, then they are right angles.
<A and <B are right angles
<A and <B are supplementary angles
<A and <B are vertical angles
<A and <B both have measure 750

22. Geometry EOCT
22. Lines p and q are both perpendicular to plane K. Plane R contains lines p and q. Which statement is true about planes K and R?
Planes K and R do not intersect.
Planes K and R are perpendicular.
Planes K and R intersect in line p.
Planes K and R are the same plane.

23. Geometry EOCT
23. If r > 0 and s < 0, in which quadrant of the xy-plane does the point (r,s) lie?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV

24. Geometry EOCT
24. In the figure below, AD=DG and AE=GC. Which of the following must be true? A. B. C. D.

25. Geometry EOCT
25. Which set of points is equidistant from the rays that form an angle?
Perpendicular bisector
Skew line
Angle bisector
Central angle

26. Geometry EOCT
26. Let C be the incenter for triangle DEF. Given m<EFD = 980 , find m<ECD.
1390
980
410
1200

27. Geometry EOCT
27. In the figure below, triangle WXY is congruent to triangle YZT. Which statement is not necessarily true?
m<WXY = m<YZT
m<WXY = m<XYZ
m<XWY = 2(m<YZT)
Segment XY is parallel to segment ZT

28. Geometry EOCT
28. A machine produces identical toys in the shape of a circle. Which term best describes the relationship between any two of these toys?
concave
concentric
congruent
tangent

29. Geometry EOCT
29. The Venn diagram below represents the set of all quadrilaterals. Which answer represents appropriate choices for X, Y, and Z, in that order?
parallelogram, trapezoid, square
parallelogram, rectangle, square
rectangle, parallelogram, square
rectangle, trapezoid, square

30. Geometry EOCT
30. Which word describes a triangle whose angles measure 240 ,370 , and 1190?
isosceles
acute
right
obtuse

31. Geometry EOCT
31. In the xy-plane, if the lines y=3 and y=2x + k intersect at (5/2,3), what is the value of k? 8 3
-7/2 -2

32. Geometry EOCT 32. Which statement about a parallelogram must be true?
All of its angles are congruent.
One pair of sides are parallel and one pair of sides are congruent.
Its opposite sides are congruent.
Consecutive angles are congruent.

33. Geometry EOCT 33. For the following triangles: What is DE? 14/3 16/7 7
None of these

34. Geometry EOCT
34. What is the measure of an angle inscribed in a circle if the intercepted arc measures 720?
180
360
720
1440

35. Geometry EOCT
35. Which number is closest to the value of x in the figure below?
Sin320 = 0.530
Cos320 = 0.848
Tan320 = 0.625
0.424
1.060
1.250
1.378

36. Geometry EOCT
36. The figure below shows two similar rectangles. What is PQ? 2 3 4 5

37. Geometry EOCT
37. A 100 ft. wire extends from the top of a pole to a point P on the ground, as shown in the figure. Which expression gives the distance, in feet, from P to the bottom of the pole?
100cos500
100sin500
Cos500 /100
Sin500 /100

38. Geometry EOCT
38. What is the length of a diagonal of a rectangle with length 12 and width 5? 7 13 17 60

39. Geometry EOCT
39. A square is dilated with a scale factor of 4. If a side of the original square is 12, what is the measure of a side of the new square? 3 8 12 48

40. Geometry EOCT
40. Points P, Q, R, S and T are different points on the circle below. Points P and R are shown. Segment PQ and segment RS are diameters of the circle. The length of minor arc PR is 1 unit, and the length of minor arc PT is one unit. What could be the clockwise order of these five points, beginning with point R.
RQSTP C. RSQTP
RQTPS D. RSTQP

41. Geometry EOCT 41. What is the value of x in the figure? 510 780 1560
1800

42. Geometry EOCT
42. A building that is 50 feet tall casts a shadow that is 30 feet long. Nearby, a tree casts a 75-foot-long shadow. How tall is the tree?
95 ft.
110 ft.
125 ft.
140 ft.

43. Geometry EOCT
43. The length of a side of a square changes by a factor of 3, what factor does the area change? 3 9 12 27

44. Geometry EOCT 44. What is the value of x in the triangle? A. B. 6
C x D.

45. Geometry EOCT
45. Quadrilateral ABCD is similar to quadrilateral PQRS. Which of the following gives x in terms of y?
x = 4/5 y
x = 4/6 y
x = 5/4 y
x = 5/6 y