Name__________________________________ Date_____________ Period_________
Geometry Midterm Review
Vocabulary:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Points that lie on the same line.
1. _________________
Having the same size, same shape
2. _________________
These are non-adjacent angles formed by intersecting lines.
3. _________________
A 12 sided polygon
4. _________________
Two angles whose measures have a sum of 90°.
5. _________________
Two angles whose measures have a sum of 180°.
6. _________________
A quadrilateral with exactly one pair of parallel sides.
7. _________________
To divide into two congruent parts.
8. _________________
A 10 sided polygon
9. _________________
This is the common endpoint of an angle.
10. ________________
A quadrilateral with 90 angles, and congruent sides
11. ________________
Points do not lie on the same line.
12. ________________
Part of a line consisting of two points and all points between them
13. ________________
A polygon that is both equilateral and equiangular.
14. ________________
The process of using logic, rules, definitions to draw conclusions
15. ________________
A triangle with at least 2 congruent sides
16. ________________
The process of reasoning that a rule or statement is true because specific cases are true (patterns)
17. ________________
18. A quadrilateral with exactly two pairs of congruent consecutive sides. 18. ________________
19. An angle that measures greater than 0 and less than 90
19. ________________
20. A line that intersects two coplanar lines at two different places
20. ________________
Using the figure at the right:
21. Name 3 coplanar points:
22. Name 3 collinear points:
23. Name the intersection of the planes
24. R is between S and T. If SR = 2x + 2, RT = x, and ST = 20. Find SR.
25. If DB bisects ADC, mADB= (3x + 6), and mBDC = (5x –4), find ‘x’.
B
C
A
D
26.In the diagram, name a pair of:
supplementary angles: _______________
vertical angles: _______________
complementary angles: ________
adjacent angles: _________
6
1
5
2
4
27.In the diagram, m1 = (2x + 15) and m2 = (x + 45). The value of ‘x’ is:
1
2
28. Find the next two terms in the sequence.
2, 4, 16, _____, _______
100, 81, 64, 49, _____, _______
29.Use the following conditional and write:
If an angle is acute then it is less than 90.
Converse(qp):_______________________________________________
Inverse(~p ~q): _____________________________________________
Contrapositive(~q~p): ________________________________________
Biconditional(if and only if): ________________________________________________
30.Identify the hypothesis and conclusion of the conditional statement.
If it is snowing than it is cold.
Hypothesis: __________________________________
Conclusion: __________________________________
B
31.Using the figure to the right, list the segments that are:
skew to AB
C
A
D
parallel to AB
G
perpendicular to AB
F
H
I
3
32. In the figure, identify a pair of:
alternate interior angles: ___________
vertical angles: ____________________
corresponding angles: _____________
alternate exterior angles: ___________
same side interior angles: __________
linear pair: _______________
1 8
2 7
4
33. Given the diagram, if lines p and q are parallel, solve for x.
3 6
5
(4x)
p
(2x + 30)
q
34. Find the value of ‘x’ so that lines p and q are parallel.
p
q
(8x)
(2x)
35. Use the distance formula to find the distance between
A (5, -2) and W (-1, 7).
36. Find the midpoint of (8, -2) and (4, -6).
37. What is the slope of the line that is perpendicular to the line whose equation is 3x- 2y = -8?
38. What is the slope of a line parallel to the line 8x - 2y = 10?
39. What is the relationship between the lines: y  3x  2 and 6x  2 y  4 ?
(parallel, perpendicular, or coinciding lines)
40. How should Annette classify this triangle?
By sides: __________________
By angles: _________________
60
60
60
41. Solve for x:
42. Solve for x:
40
60
x
2x
(4x -1)
x
43. Which postulate or theorem can be used to prove the following triangles are congruent?
B. C
F. C
F
E. A
B
A. A
D
E
___________________
___________________
D. D
C. B
___________________
44. Complete the congruent statement and state which postulate or theorem can be used to prove the 2 triangles
congruent.
∆JKL  ∆__________
M
J
K
N
L
45. Name one additional pair of corresponding parts that need to be congruent in order to prove that ∆FIG
∆TOM
by AAS: ___________
by ASA: _________
by SAS: _______
T
I
F
G
46.Given
M
O
QS  4x  5 and TV  9x  20 , find the length of QS and TV.

47. Find the value of x. The diagram is not to scale.
40
x
40
32
25
25
I
73
48. Which side is the longest side in this triangle?
J
57
50
K
49. Which three lengths could be the lengths of the sides of a triangle?
a. 10m, 5m, 12m
b.10m, 16m, 26m
c. 8m, 12m, 21m
d. 20m, 7m, 6m
50. A ladder reaches the top of a 15 ft building. The ladder is 3.5 feet away from the building on
the ground. How long is the ladder?
51. If a right triangle has a hypotenuse of 20 units and a leg with a length of 5 units, find the length
of the missing side, and leave in simplied radical form.
52. Nathan is sitting on a dock, 6 feet above the water, with a 10 ft rope attached to his toy
sailboat. How far away is the boat from the dock? Round your answer to the nearest tenth.
53. In the figures find the missing parts.
54. In the figures find the missing parts.
55.Tom is trying to put a divider diagonally to separate his animals and his play area. If he knows that each side
of his backyard is 9ft long, how many feet of fencing will he need to build a divider between them.
x
9
56. For each of the following regular Heptagon find:
a) the sum of the interior angles: _________
b) the measure of each interior angle: __________
c) the sum of the exterior angles: __________
d) the measure of each exterior angle: ___________
57. Find the values of the variables in the parallelogram. The diagram is not to scale.
29
102
y°
z°
x°
58. For trapezoid JKLM, A and B are midpoints of the legs. Find AB.
J
19
A
M
K
B
27
L
59. Answer the questions below using square ABCD.
a. If AB = 15, find DC: _______
b. Find the mAEB: _______
c. If AE = 9x - 2 and EC = 7x + 6, then x = _________
d. If DE = 3y – 2 and BE = 2y + 5, then y = _________
60.
p  10 8

p7
9
61.
62. ∆ABC ~ ∆DEF. Find the value of:
x: _____
y: _____
x
3

15 5
B
E
D
A
10
9
x
y
8
C
12
F
63. Find the value of “x”.
16
8
10

x

64. Find the value x:
65. The three angles in a triangle are in a ratio of 8:3:9. Find the measure of each angle and classify the triangle
by its angles.
66. Which constructions are being shown in the accompanying diagrams?
___________________
__________________