Name: __________________________________________________ Class Period: __________ Date: ______________ Geometry Honors Semester 1 Final Exam Study Guide Part 1 Outcome 1

- Distance - Midpoint/Find missing endpoint - Partitioning a line segment - Parallel, Perpendicular, or neither? - Write equation of a parallel line through a point - Write equation of a perpendicular line through a point

Outcome 2

- Reflect points/figures over a given line - Translate points/figures over a given vector - Rotate points/figures about a given point - Describe a translation vector in words and with a mapping - Rotate a line about a given point - Perform compositions of transformations - Write a rule for compositions of transformations

Outcome 3

- Identify corresponding parts of congruent triangles - Prove triangles congruent (SSS, SAS, ASA, AAS, HL) - Identify missing information to prove triangles congruent - Definitions, Properties, and Theorems from The Basics Packet

Outcome 4

- Properties/theorems of parallel lines - Parallel line angle pairs - Prove lines are parallel - Use parallel lines to prove other things - Prove a quadrilateral is a parallelogram - Prove a quadrilateral is a rectangle - Hinge Theorem/Converse

Outcome 5

- Distance between a point and a line - Distance between parallel lines - Simplifying Radicals - Supplementary and complementary angles** - Crook problems** - Parallel line angle pairs**

**Will only be on final exam if we cover that material in class prior to finals.

Outcome 1

Find the coordinates of the midpoint of AB .

1. A(6, 7), B(4, 3) 2. A(1, 5), B(2, 3)

The coordinates of point Y are given. The midpoint of XY is (3, 5). Find the coordinates of point X.

3. Y(0, 2) 4. Y(10, 5)

5. Given the points A(-3, -4) and B(5, 0), find the coordinates of the point P on directed line segment AB that partitions

AB in the ratio 2:3.

6. Find the coordinates of point P, that lies two-thirds of the way on the directed line segment AB , where A (-2, 5) and B (4, 9).

Distance Formula Midpoint Formula Slope Formula Slope-Intercept Form

Find the distance between each pair of points. If necessary, round to the nearest tenth.

7. A(6, 7), B(1, 7) 8. C(-5, 5), D(5, 3) Graph each figure in the coordinate plane. Find the perimeter.

9. X(4, 2), Y(2, 10), Z(2, 2)

Write an equation of the line parallel to that contains point C.

10.

; C(7, 1) 11. y = -2x + 1 ; C (0,3)

Write an equation of the line perpendicular to the given line that contains P.

12. P(4, 3) ; y = 3x 15 13. P (4,4); Determine whether the lines are parallel, perpendicular, or neither. Explain your reasoning.

14. y - 7x = 6 15. 2x + 5y = -1 16. 52

6 ( 4)y x

Y + 7x = 8 10y = -4x – 20 5y = 2x + 6

Outcome 2 17. Use a vector and a mapping to describe the translation that is 6 units to the left and 4 units up.

18. Use a vector and a mapping to describe the translation that is 7 units to the left and 1 unit down.

19. The vertices of a rectangle are R(–5, –5), S(–1, –5), T(–1, 1), and U(–5, 1). After translation, is the point (0, -

13). Find the translation vector and coordinates of .

20. Considter quadrilateral with vertices , , , and and its reflected image in

the axis. Write the correct coordinates for the new quadrilateral .

21.

22.

23.

24.

25.

26.

27.

28. Describe the translation. Then write a vector and a mapping.

29. ΔABC has vertices A(2, 2), B(3, – 2), and C(–1, 3). Graph ∆ABC and its image after a rotation 90° about the

point (4,-5).

30. The vertices of PQRS have coordinates P(–1, 5), Q(3, 4), R(2, – 4), and S(–3, – 2). Write the coordinates of its image after a rotation 90° clockwise about the origin.

31. The vertices of the image of KLMN after a 90° rotation counterclockwise are K’(–3, 2), L’(2, 3), M’(4, – 2), and N’(–2, – 4). What are the coordinates of the vertices of KLMN?

K = L = M = N =

32. Give the equation of the line

after a rotation about the point (-2,1) through a 270⁰ angle. Write

the equation of the new line. Then, describe the relationship between the equations of the image and preimage.

Graph each figure with the given vertices and its image after the indicated glide reflection. 33. ∆MPQ: M(−4, 3), P(−5, 8), Q(−1, 6) Translation: along ⟨−4, −4⟩ Reflection: in y = x

Graph each figure with the given vertices and its image after the indicated composition of transformations.

34. : A(−3, 2) and B(3, 8) Rotation: 270° about origin Translation: along ⟨-4, 1⟩, Reflection over

35. : R(2, −1) and S(6, −5) Translation: along ⟨−2, −2⟩, Reflection: in y=3, Rotation 180°

36. Describe the transformations that combined to map each figure.

Then write a composition of transformations that would map A”B”C”D” to ABCD. (You may NOT use the reverse of your transformations from the first part of the problem.) Write a single rule for this composition of transformations.

Rule: ____________________________________

Rule: ____________________________________

Outcome 3

37. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c.

b. d.

38. Name the Property that justifies the statement: If .

A B

C D

A’

B’

C’

D’

A’’

B’’

C’’

D’’

Composition of transformations:

39. Can you use the ASA Theorem, the AAS Theorem, or both to prove the triangles congruent?

40. Based on the given information, what can you conclude, and why?

Given:

41. If and , which additional statement allows you to conclude that by ASA?

42. Given: is the bisector of What can you conclude and why?

43. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

44. What else must you know to prove the triangles congruent by ASA? By SAS?

45. From the information in the diagram, can you prove ? Explain.

46. Name the angle included by the sides

and

J L

E

D

K

I

L

K

H

J

A

CB D

| |

A

CD

B

(

(

N

P

M

47. What other information do you need in order to prove the triangles congruent using the SAS Congruence Theorem?

48. Given and , find and

49. The two triangles are congruent as suggested

by their appearance. Find the value of c. The diagrams are not to scale.

50.

51. If BCDE is congruent to OPQR, then is congruent to

52.

53.

A

B C D

d°

e°f°

b

c

g

3

4

5

38°

52°

54.

55.

56.

57. Given that CXZAQB , make six additional statements of congruence.

58. Complete the congruence statements for the triangles in the following diagrams.

BAC ________ ACB ________

59. Given: PRPS TPRQPS

a. Name the additional congruent sides or angles needed to prove RPTSPQ by ASA.

b. Name the additional congruent sides or angles needed

to prove SPTRPQ by SAS.

B

C D

A

F E

D

C

B

A

P

T

S R

Q

60. Given KLM NOP KL KM OP and NP x , , , , ,25 18 23 7 17 find the value of x. Draw a diagram.

For problems 61-63, refer to the diagram and given information. Determine parts of the triangles you would be able to say are congruent, and the reason you would ultimately give for proving the triangles congruent.

61. Given: CECD

EBAD Get:

Conclusion: BCDACE Reason:

62. Given: EBFDAF

BFAF Get:

Conclusion: EBFDAF Reason:

63. Given: BCDACE

BEAD Get:

Conclusion: EBADAB Reason:

For problems 64-66, determine which postulate or theorem can be used to prove the triangles congruent. If it is not possible to prove them congruent, write “not possible.” 64. 65. 66. Outcome 4

67. Which angles are corresponding angles?

68. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary.

69. This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. How are and related?

70. WXYZ is a parallelogram. Name an angle congruent to .

F E D

C

B A

X

ZW

Y

N

71. What are the 5 reasons that guarantee that a quadrilateral is a parallelogram?

72. If and , what is ?

73.

74.

75.

1 2

3 4

5 6

7 8

b

a

c

76.

77.

78.

79.

80.

For problems 81-86, refer to the diagram. State the reason for each statement.

81. If EAGC and 64 , why is 53 ?

82. Why is 54 ?

83. If 129 and 1110 , why is GECGAC ?

84. If ADFGDB , why is 53 ?

85. If DCFD and GDDC , why is GDFD ?

86. If bisects GEC and GAC and 129 , why is GECGAC ?

87.

a. Name an altitude of ADB . b. Name a median of BDE . c. Name an angle bisector and the triangle for which it is

an angle bisector.

88. Given that DB is a median of ADC , determine whether or not it is also an altitude. Give an explanation for your answer.

89.

a. Identify a pair of corresponding angles formed by DE

and BC with transversal BE .

b. Identify a pair of alternate interior angles formed by

AC and BE with transversal BD .

c. What type of special angle pair is not pictured in the diagram?

A

B

C

D

E

F

G

1

5

6 4

3 2

8

7

12

11

10 9

C

B

E

D

A

A

D

C B

1

2 3

4 5 6

A

B C

D E

7 8 9

For problems 90-94, refer to the diagram and the given that l m and CEAB . Fill in each blank with <, >, , or

“supp”. Then give a theorem to justify your statement. Statement Justification

90. 3 ______ 15

91. 13 ______ 5

92. 8 ______ 9

93. 10 ______ 14

94. ACE _____ 12

95. Is dc ? Why or why not?

l

m

A

B

C

1 2 11

5 4 3

10 9

7 6 8

D E

12

15 14

13

c

d