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