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1st Semester Final Exam Review Name: _________________________________ Geometry Date: _____________________ Block: _____ You must show your work to receive full credit! Write your final answer on the blank provided.
Topic #1 (Foundations of Geometry) 1) Multiple Choice: The notation for the length of the segment between P and Q is __?__. _________
a. 𝑃𝑄 ⃡ b. 𝑃𝑄̅̅ ̅̅ c. 𝑃𝑄 d. 𝑃𝑄
2) Multiple Choice: Which of the following is a correct name for a plane? _________
a. W b. WX c. WXY d. WXYZ
3) Multiple Choice: Which of the following is a correct name for a line? _________
a. �⃡� b. 𝐿𝐼 ⃡ c. 𝐿𝐼𝑁 ⃡ d. 𝐿𝐼𝑁𝐸 ⃡
4) Define collinear. ______________________________________________________________________________________ __________________________________________________________________________________________________________
5) Let C be between D and E. If DC = 3v – 30, CE = 6v – 15, and DE = 27, use the v = _________ Segment Addition Postulate to solve for v. (Hint: Draw a diagram and label the given information!)
6) If mIOJ = 22° and mHOI = 25, then what is mHOJ? mHOJ = _________
7) The mJHI = (2x + 7)°, mGHI = (8x – 2)°, and mJHG = 65°. mJHI = _________ Find mJHI and mGHI. mGHI = _________
O J
H
I
H
I
J
G
8) What is the midpoint of a segment with endpoints (8, 8) and (7, 8)? _________ 9) Find the length of a segment with endpoints (4, 7) and (6, 4). _________
10) Multiple Choice: If ROS is obtuse and TOR is straight, then TOS is what _________
kind of angle?
a. Acute b. Right c. Obtuse d. Straight
11) Multiple Choice: Which does not name the angle below? _________
a. DCE b. CDE c. ECD d. C
12) In the figure (not drawn to scale), 𝑀𝑂 bisects LMN, mLMO = (13x 31)°, x = _________ and mNMO = (x + 53)°. Solve for x and find mLMN. mLMN = _________
13) If mJOK = 28° and mJOL = 58°, then what is mKOL? mKOL = _________
RT
S
O
D
EC
N
O
L
M
K
J
LO
14) The measure of an angle is 98°. Classify that angle as acute, right, _______________________ obtuse, or straight.
15) The measure of an angle is 179°. Classify that angle as acute, right, _______________________
obtuse, or straight.
16) Multiple Choice: Name an angle adjacent to AOB. _________
a. BOE b. BOC c. COD d. DOE
17) True or False: In the figure shown, mAED = 108°, Is mAEB = 72°? _______________________
18) Solve for x. x = _________
19) Define supplementary angles. _______________________________________________________________________
__________________________________________________________________________________________________________ 20) Define complementary angles. _______________________________________________________________________
__________________________________________________________________________________________________________ 21) Name a pair of vertical angles in the figure below. _______________________
22) Write the converse of the following: “If it is raining, then I should use an umbrella.”
__________________________________________________________________________________________________________
E
O D
C
B
A
B
E
C
DA
(2x+72)°
(4x+90)°
12
43
F
D
C
G
HE
B
A
Topic #2 (Parallel and Perpendicular Lines) 23) Define coplanar. ______________________________________________________________________________________
__________________________________________________________________________________________________________
24) Multiple Choice: In the figure shown below, 𝐴𝐷 ⃡ and 𝐻𝐺 ⃡ are __?__. _________
a. Parallel b. Skew c. Congruent d. Perpendicular
25) Name a plane that is parallel to plane AEF. _________
26) Multiple Choice: In the figure below, 6 and 3 are __?__. _________
a. Alternate Exterior b. Same-Side Interior c. Alternate Interior d. Corresponding
27) Multiple Choice: In the figure below, 6 and 2 are __?__. _________
a. Alternate Exterior b. Same-Side Interior c. Alternate Interior d. Corresponding
F
D
C
G
HE
B
A
8 75
4 321
6
8 75
4 321
6
H G
FA B
C D
E
75°
Q
R
P
1
S
28) If 𝑃𝑄 ⃡ ||𝑅𝑆 ⃡ , find m1. m1 = _________
29) Multiple Choice: In the figure below, 𝐻𝐶 ⃡ ||𝐺𝐷 ⃡ and mABC = 100°. _________ Which of the following statements is false?
a. mCBE = 80° b. mDEF = 80° c. DEB and CBE are corresponding angles d. CBE and GEB are alternate interior angles
30) Use the figure below to find m6. m6 = _________
31) Use the figure below to find m4. m4 = _________
32) What is the slope of a line perpendicular to y = 7x + 13? _________ 33) What is the slope of a line parallel to y = 6x 1? _________
34) Find the slope of the line between (5, 2) and (13, 6) _________
21
43
65
124° 7
742°
5634
12
55°
(x 10)°(2x)°
48°x°
21°
35) Write an equation of a line in slope–intercept form that passes through (1, 4) and is:
a. Parallel to 𝑦 = −1
3𝑥 − 4 _________________________
b. Perpendicular to 𝑦 = −1
3𝑥 − 4 _________________________
36) Find the value of x. x = _________
37) Find the value of x. x = _________
38) Find the value of x. x = _________
39) Find the value of x. x = _________
(x 15)°
x°
31°
x°
66° 117°
Topic #3 (Transformations) 40) Multiple Choice: Which of the following shows a triangle and its image _________
transformed by 𝑅𝑥−𝑎𝑥𝑖𝑠? a. b. c. d.
41) Give the coordinates of the points after the following transformation: 𝑅(270°,(0,0))
A(–2, 7) A’(_______, _______) B(0, 1) B’(_______, _______) C(3,–8) C’(_______, _______)
42) Give the coordinates of the points after the following transformation: 𝑟(90°,(0,0))
A(–2, 7) A’(_______, _______) B(0, 1) B’(_______, _______) C(3,–8) C’(_______, _______)
43) Give the coordinates of the points after the following transformation: 𝑟(180°,(0,0))
A(–2, 7) A’(_______, _______) B(0, 1) B’(_______, _______) C(3,–8) C’(_______, _______)
44) Give the coordinates of the points after the following transformation: 𝑇<2,−6>
A(–2, 7) A’(_______, _______) B(0, 1) B’(_______, _______) C(3,–8) C’(_______, _______)
45) Give the coordinates of the points after a dilation with a scale factor n = 2.5 A(–2, 7) A’(_______, _______) B(0, 1) B’(_______, _______) C(3,–8) C’(_______, _______)
46) Multiple Choice: Describe in words the transformation represented by the _________
following composition: (90 ,(0,0)) 4,2r T XYZ
a. Translation left 4, up 2 followed by a rotation of 90° clockwise about the origin b. Rotation of 90° clockwise about the origin followed by a translation left 4, up 2 c. Translation left 4, up 2 followed by a rotation of 90° counterclockwise about the origin d. Rotation of 90° counterclockwise about the origin followed by a translation left 4, up 2
47) Multiple Choice: Describe in words the translation represented by 𝑇<6,−3> _________
a. 3 units to the left, 6 units up b. 6 units to the left, 3 units up c. 3 units to the right, 6 units down d. 6 units to the right, 3 units down
Topics #4–5 (Triangles) 48) Describe a congruence transformation that maps YFC to PVG.
49) Multiple Choice: If MNO VWX, which statement is NOT true? _________
a. 𝑁𝑂̅̅ ̅̅ ≅ 𝑉𝑊̅̅ ̅̅ ̅ b. 𝑀𝑂̅̅ ̅̅ ̅ ≅ 𝑉𝑋̅̅ ̅̅ c. O X d. N W 50) Given LMN UVW, complete the statements to the right. 𝑈𝑊̅̅ ̅̅ ̅ _________
VWU _________ 51) Identify the congruence postulate/theorem that proves the triangles _________
congruent (SSS, SAS, ASA, AAS, or HL). Then, complete the congruence JHZ _________ statement.
52) Multiple Choice: What must be true in order for ABC EDC by SAS? _________
a. 𝐴𝐶̅̅ ̅̅ ≅ 𝐶𝐸̅̅ ̅̅ b. 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐸̅̅ ̅̅ c. B D d. A E
A
EB
D
C
V
Z
J
H
53) Multiple Choice: Refer to the figure below. Which of the following statements _________
is true?
a. TUV XWV by ASA b. TUV VWX by SAS c. TUV WXV by SAS d. TUV XVW by SSS
54) State the two congruence postulates/theorems (SSS, SAS, ASA, AAS, or HL) _________
that can be used to prove that AOB COD. _________
55) Name the congruence postulate/theorem (SSS, SAS, ASA, AAS, or HL) _________
that proves ABD CBD.
56) Identify the congruence postulate/theorem that proves the triangles _________
congruent (SSS, SAS, ASA, AAS, or HL). Then, complete the congruence NMO _________ statement.
D
C
B
A
R
P
N
M
O
C
D
B
O
A
T
X
WV
U
57) In the diagram below, 𝐴𝐶 ⃡ is the perpendicular bisector of 𝐵𝐷̅̅ ̅̅ . x = _________ If BD = 36, find the value of x, ED, AD, and DC. ED = _________ AD = _________
DC = _________
58) Find the measure of each base angle in the isosceles triangle below. _________
59) Find the value of x in the isosceles triangle below. x = _________
60) Multiple Choice: Which of the following could be sides of a triangle? _________
a. 15 cm, 4 cm, 20 cm b. 3 cm, 15 cm, 20 cm c. 11 cm, 5 cm, 16 cm d. 5 cm, 12 cm, 16 cm
61) In ABC, AC = 9, CB = 10, and AB = 11. Identify the largest angle of ABC. _________
40°
2525
30°x°
18
15
3x ED
C
B
A
Topic #6A (Quadrilaterals) 62) Name the figure shown below. _______________________
63) Complete the table below naming each polygon based on the number of sides. # of
Sides Type of Polygon
3 4 5 6 7 8 9
10 12 47
64) Three angles of a quadrilateral are 113°, 66°, and 67°. What is the measure _________
of the missing angle.
65) Find the values of x and y. x = _________ y = _________
66) Find the values of x and y. x = _________ y = _________
67) In parallelogram LMNO, ON = 7x 5, LM = 6x + 3, NM = x 4, x = _________ and OL = 2y + 5, find the values of x and y. y = _________
65°
126°y°
114°x°
114°
x°
y°
72° 68°
68) In the parallelogram below, TA = 6x - 7 and TG = 23. Find the value of x. 69) Find the value of x in the parallelogram below.
70) Find the values of x and y in the parallelogram below.
71) Decide if you can prove if each figure is a parallelogram. Justify your answer.
a. b. c. d.
97° (11x 5)°
(2x+12)°
(4y)° (3x 18)°
(5x 42)°
G
T
VA
L