Name__________________________

Semester 1 Final Exam Review

____ Target 1: Vocabulary and notation

1. Find the intersection of 𝑀𝑁 ⃡ and 𝐿𝑂 ⃡ . 2.

3) Vocabulary: Define the following terms and draw a diagram to match:

a) Point

b) Line

c) Plane

d) Ray

e) Opposite Ray

f) Parallel Lines

g) Perpendicular Lines

h) Acute Angles

i) Obtuse Angles

j) Right Angles

k) Straight Angles

l) Adjacent Angles

m) Coplanar

n) Collinear

_____ Target 2: Segment/Angle Addition Postulate

4) 5)

____ Target 3: Translations

7.

________________________________________

9. The point Z’(2, -3) is the image under the translation (x, y) (x + 3, y - 2). What is the preimage?

Z (______, ________)

_____ Target 4: Reflections

10. 11.

12. Write the rule that describes the transformation.

Given quadrilateral S (1, 2), H (3, 1), O (4, -1), P (2, 0), translate it according to the rule (x, y) (x + 4, y -2). What are the coordinates of the image? S’ _______ H’_______ O’_______ P’_______

8. Write the rule that translates the preimage to

the image.

Patty performed a reflection across line m. Did she do it correctly? If yes, use correct mathematical vocabulary to convince me she did. If no, use correct mathematical vocabulary to tell me she did not.

____ Target 5: Naming Angle Pairs

13) Given a || b cut by a transversal c, which of the following statements is not true.

A) 1 and 3 are corresponding angles B) 2 and 3 are same-side int. angles C) 3 and 4 are vertical angles D) 1 and 4 are alternate int. angles

14) Refer to the diagram.

A) Name a pair of same-side interior angles.

B) Name a pair of corresponding angles.

C) Name a pair of alternate interior angles.

_____ Target 6: Rotations

_____ Target 7: Symmetry

18. Given a regular 4-sided polygon (also known as a square), answer the following questions:

a. How many lines of symmetry does it have? __________________________

b. Does it have point symmetry? _____________________________________

c. What is the minimum number of degrees it will take to rotate the figure onto itself? _____________________

_____ Target 8: Compositions

19. Reflecting an object in two parallel lines will result in a (pick 1)

a. reflection b. translation c. rotation d. dilation

15. Rotate the figure 90° CCW

about the origin.

16. Rotate the figure 90°

CW about point C.

17. Rotate the figure 90°

CCW about the point (2, 3)

20. Reflecting an object in two intersecting lines will result in a (pick 1)

a. reflection b. translation c. rotation d. dilation

21. Graph the figure B(-3, -2), A(-4, -4), T(-2, -4) then perform the glide reflection according to the rules

(x, y) (x -3, y) and reflect across y = -4.

Target 9: Slope

Determine whether the pair of lines is parallel, perpendicular, or neither.

22. 2x + 3y = 7 23. 2x + 3y = 7 24. 2x + 3y = 7

y = -3/2x – 4 y = 3/2x – 4 -2x-3y = -1

_____ Target 10: I can write the equation of a line. (Pick either form)

25. Write the equation of the line through the points (-1, 3) and (0, 4)

26. Write the equation of the line in slope intercept form parallel to 3y = -x + 2 through the point (-3, -2).

27. Write the equation of the line in point-slope form perpendicular to y = 2x - 2 through the point

(-2, 3).

_____ Target 11: Angle pairs with algebra

28. Find the measure of the numbered angles.

m∠1 = ___________

m∠1 = ___________

m∠1 = ___________

m∠1 = ___________ m∠2 = ___________ m∠3 = ___________ m∠4 = ___________

29. Find x

____ Target 12: Proofs with parallel lines

30. Using transformations, show that a||b

31. Given a || b cut by a transversal c, which of the following statements are not true.

A) 1 ≅ 3 B) 2 ≅ 3 C) 3 ≅ 4 D) 1 ≅ 4

____ Target 13: Dilations

34. Is ΔE’F’G’ a dilation of ΔEFG?

Claim: ____________________________

Evidence:

Conclusion:

Is ΔE’F’G’ a dilation of ΔEFG? _____________________________________________

Reasoning (Use specific examples from your evidence):

Segment Slope Length

32. Dilate the cow by a scale

factor of 3 centered at the

origin.

33. Dilate the cow by a scale factor of ½ centered at (2, 1).

C ( -2, 0)

O (0, 2)

W (2, 0)

C(-2, 1)

O (-4, 3)

W (-2, 5)

3 ft

9 ft

11 ft

5 ft

Target 14: Similar polygons with algebra

35) The two rectangles are similar. Which is a correct proportion for corresponding sides?

a.

b.

c.

d.

36) The skyscraper in Chicago is 1450 feet high. A model of the skyscraper is 24 inches tall. What is the ratio of the

height of the model to the height of the actual skyscraper?

37) Solve the proportion.

38) The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second.

The figures are not drawn to scale.

39) Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.

40) You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what

will be the dimensions of your scale drawing?

x

8 m

4 m

12 m

15 18

41) Figure . Name a pair of corresponding sides?

42) ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find ZY. The figures are not drawn to scale.

43) Triangles ABC and DEF are similar. Find the lengths of AB and EF.

44) Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram.

What is the distance between the two campsites? The diagram is not to scale.

45) Find x and y, given that .

A

B C

D

FE

4

55x

x

B

A

C

P Q

8

x 18

12

16

y

R Q

P

21

20

29

Not drawn to scale

46) Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Not drawn to scale

____ Target 15: Proving triangles are similar

State whether the triangles are similar. If so, write a similarity statement, the similarity ratio and the postulate or

theorem you used.

47) a. b. In ABC, AB = 8, AC = 10 and A = 24o. In

DEF, DE = 12, DF = 15 and D = 24o.

Similar? __________________________________ Similar? _______________________________

Similarity Statement_________________________ Similarity Statement ______________________

Reason ___________________________________ Reason _________________________________

Target 16: SOH CAH TOA/Pythagorean Theorem/Right Triangle stuff

48) Find the length of the missing side. The triangle is not drawn to scale.

49) Write the tangent ratios for and .

30°

x y

20

25

24

50) Find the value of x. Round to the nearest tenth.

51) MK is the bisector of AB. Find the value of each variable. (not drawn to scale)

______ Target 17: Angles of elevation and angles of depression

52) A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-

foot-long shadow. Find the angle of elevation to the nearest degree.

53) A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance

door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance

door?

______ Target 19: Properties of congruency

54) If ∆𝐷𝐿𝑄 ≅ ∆𝐸𝑀𝑅, then which of the following are not true?

A) MRELDQ B) EMRDLQ C) QLDRME D) LQDMRE

55) ∆𝑋𝑌𝑍 ≅ ∆𝐴𝐵𝐶. What angle is congruent to ?Y

10

x

Not drawn to scale

____ Target 20: Proving triangles are congruent

56) State the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot be proven

congruent, write not possible.

57) Name a pair of overlapping congruent triangles. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or

HL.

58) Which two sides must be congruent to use ASA to prove JCXDMX ?

59) Which two angles must be congruent to use SAS to prove CBXADX ?

60) Are the triangles congruent? If so, write a congruence statement and justify your reasoning. If not, write not

congruent.

61) Given: 𝐴𝐵 || 𝐷𝐶

𝐴𝐷 || 𝐵𝐶

Prove: ∆𝐴𝐷𝐶 ≅ ∆𝐶𝐵𝐴

62) Given: 𝐸𝐼 and 𝐻𝐹 bisect each other at G.

Prove: E ≅ I

63) Given: JKMJ

MLKL

MLJK

Prove: KLJM