Name:
Date:
Geometry
Midterm Review
You must show all work to receiver full credit and earn a total of 5 bonus points on
midterm.
Chapter 1: Foundations of Geometry
1) Name the Plane:
R
2) Name 3 collinear points:
I
A
3) Name 3 non-collinear points:
F
4) Name all the rays in the plane:
5) If E is the midpoint of DF , DE = 2x + 4 and EF = 3x -1. Find DE, EF, and DF.
DE =___________________
EF=____________________
DF=____________________
6) Find the length of KL.
K 2.5x
L
x
M
_____________5x-3_________________
KL=____________________
7) T is in the interior of <PQR. Find each of the following.
a. m<PQT if m<PQR= 35º and m<RQT =10 º.
________________________
b. m<PQR if m<PQR= (2x+35)º, m<RQT = (x-5)º and m<PQT = (6x +10)º
________________________
c. m<PQR if QR bisects <PQR, m<RQT = (3x+8)º and m<PQT = (9x-4)º
________________________
8) 8) <DEF and <FEG are complementary. m<DEF = (5y +1) º, and
m<FEG = (3y-7)º. Find the measure of both angles.
m<DEF=________________
m<FEG=________________
9) <DEF and FEG are supplementary. m<DEF = (3z+12) º and m<FEG = (7z-32)º.
Find the measures of both angles.
m<DEF=_______________
m<FEG=________________
2x + 5
10) Use your knowledge of vertical angles to solve for x.
1
2
4x -5
11) What is the angle measure of <1 & < 2?
12) Find a counterexample to show the conjecture is false. “Any number divisible by
two is also divisible by 4.”
A)
8
B)
16
C) 18
D) 20
13) If two lines intersect, they intersect in exactly ____________________________.
14) If two planes intersect, they intersect in exactly ___________________________.
15) Find the circumference and area of the circle with radius of 25. Use 3.14 for pi.
Round to nearest hundredth if necessary.
C = ______________
A = ______________
16) Find the area of the polygon.
12 ft
5ft
9ft
15ft
A = ______________
17) If <A and <B are supplementary angles and m< A = ½ m<B, find m<A and m<B.
m<A = ___________
m< B = ___________
18) Bisect the <ABC
A
B
C
Chapter 2: Geometry Reasoning
19) Write the converse, inverse, and contra positive of the conditional statement “If
Stephanie’s birthday is January 1st, then she was born on New Year’s Day.” Find
the truth value of each.
20) For the conditional “If an angle is straight, then its measure is 180 degrees,” write
the converse and the bi-conditional.
21) Determine if the bi-conditional “x2 = 100 if and only if x = 10” is true. If false,
give a counterexample.
22) Test the statement to see if it is reversible. If so, write as a true bi-conditional
statement. If not, write not reversible. “If lines intersect they intersect in exactly
one point” is true. If false, give a counterexample.
23) Write the conditional, converse, inverse and contra positive of the statement: All
rectangles has four right angles.
24) Write the definition “A scalene triangle is a triangle with three different side
lengths” as a bi-conditional.
25) Change the following statement to a conditional statement: All even numbers are
divisible by 2.
26) Identify the hypothesis and conclusion of the conditional. A triangle with one
angle greater than 90 degrees is an obtuse triangle.
27) Write the converse of the statement: “If it is Memorial Day, I do not have to go to
school.”
28) Are the following statements true or false? If false, provide a counterexample.
a. If it is Monday, then I have to go to school.
b. If you have two right angles, then the angles are congruent.
c. If a number is divisible by 3, then it is also divisible by 9.
d. If you each a piece of fruit, then it must have seeds.
Chapter 3: Parallel and Perpendicular lines
29) Name all the segments that are parallel to BC
E
F
C
D
30) Name all segments that are perpendicular to BC
H
31) Name a pair of skew lines.
A
32) Name a pair of parallel planes.
G
B
k
1
2
m
3 4
5 6
7 8
mn
n
Use the diagram above for questions # 33 -44
33) Name all pairs of vertical angles.
34) Name all pairs of same side interior angles
35) Name all pairs of corresponding angles.
36) Name all pairs of alternate interior angles.
37) Name all pairs of alternate exterior angles.
38) Name all pairs of same side exterior angles.
39) Name all angles that are supplementary to < 1.
40) Line k is a transversal line of m and n. Name a pair of angles whose equality
would guarantee that line m is parallel to line q.
Then find the angle measures. Use the diagram above.
41) m<4 = (8x – 34 )°; m<5 = (5x + 2)°
m< 4 = ____________
m<5 = ____________
42) m<1 = (23x + 11)°; m<7 = (14x + 21)°
m<1 = ____________
m<7 = ____________
43) m<2 = (7x – 14)°; m<6 = (4x + 19)°
m< 2 = ____________
m<6 = ____________
44) m<1 = (6x + 24)°; m<4 = (17x – 9) °
m< 1 = ___________
m< 4 = ___________
s
r
7
1
8
6
4 5
2 3
Use the diagram above for the following questions. Use the theorems and given
information to show that r s .
45)  1  5
Converse of __________________________
46) m  3  m  4  180
Converse of __________________________
47)  3  7
Converse of __________________________
48) m  4  (13 x  4); m  8  (9 x  16); x  5
m<4 = __________________
m< 8 = __________________
Converse of _________________________
49) m  8  (17 x  37 ); m  7  (9 x  13); x  6
m<8 = __________________
m<7 = __________________
Converse of _________________________
50) m  2  ( 25 x  7 ); m  6  ( 24 x  12); x  5
m<2 = __________________
m<6 = __________________
Converse of _________________________
51) Given: p q
Prove: m  1  m  3  180
1
2
p
52) Given: l m,  1  3
1
Prove: r p
l
3
q
2
p
3
r
m
Chapter 4: Triangle Congruencies
53) Label each diagram appropriately and identify which triangle congruence theorem
satisfies the diagram. Choose from SSS, SAS, ASA, AAS, HL or not possible. If
it is not possible explain why. Show all work; put a box around your answer.
Triangles are not drawn to scale.
a. Prove ABD  ACD
A
B
C
D
b. Prove ADC  ABC
D
C
A
B
c. Prove ABC  DEC
A
A
B
A DEC
d. Prove ABC 
D
A
E
A
C
A
A
B
C
E
D
B
C
Prove: ΔAEB  ΔCED
54) Given: AC bisects BD
BD bisects AC
Prove: ΔAEB  ΔCED
E
A
Statement
D
Reason
Given
Given
DE  BE
AE  CE
AEB  DEC
QED
B
55) Given: AB  BC
BD  AC
Prove: ABD  CBD
A
D
C
M
MJ  NJ
 MJK  NJK
Prove: MK  NK
56) Given:
K
J
N
57) Find the measure of each angle.
(2x+19)º
(x+5)°
3x°
58) Find the measure of x.
(2x + 3)°
(4x -7)°
N
Chapter 5: Properties and Attributes of Triangles
59) Find the measure of <R and <P.
P
(2x-10)º
R
m<R:_____________
(4x -34)º
Q
m<P:_____________
60) Find the value of x.
(x)º
Decide which of the triangles with the lengths below are right triangles.
Support your answer using the Pythagorean Theorem.
61) 6 ft, 8 ft, 10 ft
62) 8 m, 10 m, 12 m
63) 11 cm, 14 cm, 17 cm
64) Solve for the missing side. Round to nearest tenth if necessary.
8 ft
3 ft
.
65) Solve for the missing side. Round to the nearest tenth if necessary.
20 ft
15 ft
66) Sir Shrek is off to rescue Princess Fiona in the highest tower of the castle. He
shoots an arrow with a 75 foot rope attached to it, to the top of the tower. Shrek is
stand 20 feet away from the tower when he shoots the arrow. How tall is the
tower he has to climb in order to rescue Princess Fiona?
67) Find the perimeter of a square with a diagonal 20 cm long.
68) If Triangle ABC is congruent to Triangle DEF, state all segments and angles that
are congruent.
69) Solve for x.
9
12
60°
60°
x
70) Find the length of line segment CD, if AB = 26; AE = 10 and m<C = 45°.
A
B
C
E
F
D