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Honors Geometry
Mid Term Exam Review
Name__________________________________________
Date____________________ period__________
1. What is a linear pair? Draw an example.
2. In the below, what is the value of x?
In the diagram , m2=60. What must the m6 equal in order for y z ?
3.
4. In the diagram ,
l m . Describe the relationship between 4 and 15 and name the pair.
5. State a possible conclusion based on the following statement: If p  q and q  r , then ___
What law is being illustrated?
65º
80º
30º
6.
xº
In the diagram , what is the value of x?
85º
50
7. In the diagram , find mA.
intersecting road
A
74°
highway
xº
8.
4x-12
2x
The Department of Transportation wants to extend the intersecting road across the highway as
indicated by the dotted line. What should x be to ensure that the intersecting road and the new
construction form a straight line?
9. Two parallel sections of pipe are joined with a connecting pipe as shown. What is the value of x?
X
a
1 2 3
10.
W
In the diagram , if 3  Y , what is the relationship of 1 and W? Why?
l
Y
120º
11. In the diagram , line l intersects lines w, x, y and z, forming angles with measures as indicated.
Which two lines are parallel?
(6x–21)º
w
x
70º
y
l
12. What value for x will make m parallel to l?
70º
110º
(3x)º
m
13. Write the contrapositive of the following conditional statement: If you do your homework, then you will be prepared for the test.
z
X
14.
V
R
Y
In the diagram , mYZV=40 and mXYZ=65. Which angle must equal 40 in order for
VR YZ ?
Z
2
15. In the diagram , what condition will guarantee that line l is parallel to line m?
3
1
4
l
t
6
m
16.
n
7
5
m
8
1 2
3 4
In the diagram , parallel lines (m and n) are cut by transversal t. If m1=3x+6 and m6=2x-1, what is the value of x?
5 6
7 8
17. The measures of two complementary angles have a difference of 26. Find the measure of each angle.
18. List one possible conclusion based on the diagram .
Isosceles
Triangles
Equilaterals
Triangles
19. Write the conclusion that logically follows the following statements.
If negotiations fail, the baseball strike will not end.
If the baseball strike does not end, the World Series will not be played.
20. Consider the following statements:
p:
q:
0
The sum of two angles is 90
The two angles are complements
Write a statement using appropriate symbols to represent:
0
If two angles are not complements, then the sum of the two angles is not 90 .
21. List three possible conclusions based on the diagram below.
Pet Owners
dog owners
cat owners
bird owners
22. Which list could not be the measures of lengths of the three sides of a given triangle?
A 15 in, 12 in, 15 in
B 22 ft, 23 ft, 10 ft
C 17 cm, 16 cm, 39 cm
D 11 m, 8 m, 6 m
23. Consider the following arguments. If the first 2 statements are true, in which argument is the 3 rd statement an incorrect conclusion?
A
1. If it rains, then we will stay inside.
2. If we stay inside, then we will play games.
3. If it rains, then we will play games.
C
1. If Susan eats her broccoli, then she will get ice cream.
2. If Susan gets ice cream, then she will stay up late.
3. If Susan eats her broccoli, then she will stay up late.
B
1. If we win the game, then we will win the championship.
2. If we win the championship, then we will get a trophy.
3. If we do not get a trophy, then we did not win the game.
D
1. If John studies, then he will pass the test.
2. If John passes the test, then he will not be grounded.
3. If John is grounded, then he will study.
24. Which triangle is not congruent with the other 3?
A
B
C
D
25. In the diagram , M is the midpoint of LN and KP . What reason can be used to prove KMLPMN?
D
26. In the diagram , AD  AC and AB  AE .
Which postulate/theorem can be used to prove
B
A
27.
ADB  ACE ?
E
F
A
Given: ACBD; ADBC
B
C
E
C
D
What reason could be used to prove
DCA CDB
28. In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral ABC.
The perimeter of ABC is 36 cm. What is the length, in centimeters, of EF ?
29. In
DEF , mDE  8in, mEF  6in and mDF  10in. List the angles in order from largest to smallest.
30. Three boys are in a field flying kites. Viewed from above, the angle at Kyle, K, measures 45,
and the angle at Jake, J, measures 65. List the distances between each boy from least to greatest.
X
72
Y
81
Z
B
33. In ABC, mA=65, mB15, mC=100. List the sides in order from shortest to longest.
m
A
6
55
32. The locations of three water pumping stations form a triangle on a map of the area. The distance from
Station A to Station B is 650m. The distance from Station B to Station C is 556m. What is the range for the
possible distance from Station A to Station C?
65
0m
63
31. In the triangle, which angle has the least measure?
C
34. What is the first step to constructing a bisector of a segment?
35. What construction does the figure illustrate?
36.
37. Given
What construction does the figure illustrate?
ABC below, which would be the next step when constructing the bisector of
ABC?
38. Which would be the next step when constructing a congruent angle?
39. What construction does the figure illustrate?
40.
Which point lies on the angle bisector of the angle? P Q R or S ?
41. Which of the following points lies on the line that is perpendicular to
42. What is the next step in bisecting the given segment?
and passes through P?
Simplify completely in radical form:
43)
63
44)
8  72
46) Find the missing side of the given right triangle.
45)
2 6 3 15
6
47) What is the area of the triangle in #46?
4
48) Find the missing side of the given right triangle. 24
26
49) What is the perimeter of the triangle in #48?
y
10
8
6
4
2
50) What are the coordinates of the midpoint of AB ?
–16–14–12–10 –8 –6 –4 –2
–2
–4
(–12, –6) –6
A
–8
(4, 6)
B
x
2 4 6 8 10 12 14 16
51) The coordinates of the midpoint of AB are (5,9) , and the coordinates of A are (3,14) . What are the coordinates of B ?
B
52) What is the distance between points (-4, 3) and (2, 1)?
y
6
5
53) What is the slope of the line passing through points (-3, 2) and (5, -8)?
4
3
A
What is the exact length of diagonal
AC ?
5
4
3
2
1
55) Which is the slope of the line graphed?
–6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
2
1
54) Parallelogram ABCD is placed on a coordinate grid as shown.
C
–6 –5 –4 –3 –2 –1–1
y
1
2
3
4
5
6
x
–2
–3
D
–4
–5
–6
1 2 3 4 5 6
x
56) Describe the relationship of the slopes of parallel lines. If the slope of a line is 
2
, what is the slope of the line parallel to that
3
line?
57) Describe the relationship of the slopes of perpendicular lines. If the slope of a line is
5
, what is the slope of the line
4
perpendicular to that line?
58) The intersection of two planes forms a_____.
59) Two angles are vertical and complementary. Sketch the given and fill in all angle measures.
60) Find x and y. (not drawn to scale) What is the measure of each angle?
3x - 4
y
48
61) What does the FIRST C stand for in CPCTC?
62) Find the value of x for the following diagram:
(not drawn to scale)
3x - 2
88
43
2x +1
63) Complete the following proof:
Given:
105
D
A
AB CD , B  D
Prove: ABCCDA
B
C
64) Using the Law of Syllogism, If x ~c, ~f d, h c, k ~d, ~h~f ;
then x 
65) Sketch a Venn Diagram to solve the following problem:
In a private school, playing sports is mandatory. For one particular school, 60 boys play football, 30 play baseball, and 20 play
basketball. 10 boys play football and baseball. 8 play football basketball. 5 play basketball and baseball. 3 boys play all three sports.
How many guys play only baseball?
66) The vertices of a triangle are A(5, 3), B(-1, 1) and C(1, –5) Find the length of AC, the slope of AB, and the midpoint between B
and C.
67) For an octagon, find the sum of the interior angles, each interior angle, the sum of the exterior angles, and each exterior angle
measures.
68) Classify the following triangle by sides and by angles if each of the angles measure: 45, 45,90
69) Classify the following triangle by sides and by angles if each of the sides measure: 4cm, 6cm, 9cm
70) Sketch skew lines AB and
71) Sketch
CD
AB  BC
72) Given ABCXYZ, the A _______ and ZX  ______
More on polygons and congruence but we just took a test on it.