Fall 2017 Final Exam Review Academic Geometry P a g e | 1

Final Exam Review

Name: ______________________________________ Period:____________ **Show your work or you will NOT receive extra credit on your final- ONE point per side completed**

Use the diagram below to answer questions 1-6. Given: , ∠

85°

1. Give another name for . _______

2. List a pair of supplementary angles: ____________ 3. List a pair of complementary angles: _____________

4. ∠ = _______ ∠ _______ ∠ = _______

5. *Given that ∠ = 5 4 ° and ∠ = 1 °, then ∠KHB = _______

6. ∗ Given that ∠ = 12 15 °, then = _______

7. Solve for each segment using the figure.

a. *If M is between K and Q, = 8, = 6 2, and = 35 then = _______ and = _______.

b. *If M is the midpoint of , = 8 and = 6 2, then = _______

c. *If M is the midpoint of , = 4 and = 7 18, then = _______

Use the figure below to fill in the appropriate answer for questions 8-15.

8. List each pair of alternate interior angles: ______________ and ______________

9. ∠5 & ∠8 are _________________________ angles.

10. ∠4 & ∠______ are consecutive or same side interior angles.

11. ∠2 &∠6 are __________________________________________________ angles.

12. *If ∠5 = 125°, then ∠3 = ______.

13. *If ∠3 = 7 10 ° & ∠6 = 26 °, then = ______.

14. *If ∠4 = 3 11 ° & ∠6 = 25 °, then = ______.

K Q M

A

D

F

C

E

H

G K

B

J

1 2

3 4

5 6

7 8

Fall 2017 Final Exam Review Academic Geometry P a g e | 2

15. *Determine if each pair of triangles are congruent, and state the postulate or theorem used. a. b. c. d.

e. f. g. h.

Use the following conditional statement to choose the best answer for questions 16-18. Write your answer choice in the box on the left of each question. If two triangles are similar, then their corresponding angles are congruent.

16. The inverse of the statement above is: a. If the corresponding angles of two triangles are congruent, then the two triangles are similar. b. If two triangles are not similar, then their corresponding angles are not congruent. c. If the corresponding angles of two triangles are not congruent, then the two triangles are not similar. d. If two triangles are similar, then their sides are proportional.

17. The converse of the statement above is: a. If the corresponding angles of two triangles are congruent, then the two triangles are similar. b. If two triangles are not similar, then their corresponding angles are not congruent. c. If the corresponding angles of two triangles are not congruent, then the two triangles are not similar. d. If two triangles are similar, then their sides are proportional.

18. The contrapositive of the statement above is: a. If the corresponding angles of two triangles are congruent, then the two triangles are similar. b. If two triangles are not similar, then their corresponding angles are not congruent. c. If the corresponding angles of two triangles are not congruent, then the two triangles are not similar. d. If two triangles are similar, then their sides are proportional.

19. Give a counterexampe to the following statment: ℎ , ℎ . 20. *Calculate the distance between points (-5, 8) & (4, -6). d = ___________

21. *Determine the coordinates of the midpoint of the segment with endpoints (6, -9) & (1, 2). midpoint: ___________

Fall 2016 Final Exam Review Pre-AP Geometry P a g e | 3

24. *Complete the flow chart proof.

Given: is the midpoint of ; ≅ Prove: ∠ ≅ ∠

25. *Complete the two-column proof.

Given: ≅ ; bisects ∠

Prove: ∠ ≅ ∠

Statements Reasons 1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

26. *Given: ∠ = 2 18 °, ∠ = 5 , and ∠ = 10 22

∠ = _______ ∠ = _______ ∠ = _______

27. *Line passes through the points 1, 2 and 5, 0 . Write the equation of a line that is perpendicular to line and passes through the point 1, 7 .

28. *Line passes through the points 4, 1 and 3, 8 . Write the equation of a line that is parallel to line and passes through the point 6, 2 .

A

B C

A

B

C D

E

F H

Fall 2017 Final Exam Review Academic Geometry P a g e | 4

Complete the following composite transformations.

27. *Pre-image 6, 3 28. *Pre-image 6, 3

Rotate 270° ′ ________, _________ Reflect across the x-axis ′ ________, _________

Reflect across y = x ′′ ________, _________ Rotate 180° ′′ ________, _________

Translate ⟨ 2, 8⟩ ′′′ ________, _________ , → , ′′′ ________, _________

Describe each transformation.

29. 30.

_____________________________ _____________________________

31. Three roads intersect to form the sides of a triangle. There is buried treasure located equidistant to each road.

What is the name of the point where the treasure is buried? __________________________.

32. Three towns form the vertices of a triangle. There is buried treasure located equidistant to each town.

What is the name of the point where the treasure is buried? __________________________________.

33. The orthocenter is located at the intersection of the ______________________________. 34. The centroid is located at the intersection of the ______________________________. 35. The incenter is located at the intersection of the ______________________________. 36. The circumcenter is located at the intersection of the ______________________________.

37. What is the segment called? 38. What is the segment called?

39. What is the segment called? 40. What is the segment called?

41. What is the point of concurrency? 42. What is the point of concurrency?

Fall 2017 Final Exam Review Academic Geometry P a g e | 5 State each theorem and draw a picture:

43. The Triangle Midsegment Theorem:

44. The Exterior Angle Theorem:

45. The Isosceles Triangle Theorem:

46. What type of quadrilateral is Quad ABCD to the right? ________________________ * If ∠ = 61° and ∠ = 98°, find:

∠ = _______ ∠ = _______ ∠ = _______ ∠ = _______

47. * .

a. If = 11 and MN = 7, then XY = _______

b. If = 10 2, = 21, and = 8 19, then = _______

c. If ∠ = 58°, then ∠ = _______ and ∠ = _______

48. *Given the figure to the right is a parallelogram, find the missing variables.

= _______ = _______ = _______

49. * .

a. If ∠ = 67°, then ∠ = _______ b. If ∠ = 135°, then ∠ = _______ c. If ∠ = 2 8 °, then = _______ d. If ∠ = 5 15 ° and ∠ = 7 19 °, then = _______

50. * . a. If ∠ = 28°, then ∠ = _______

b. If ∠ = 16 26 °, then = _______

c. If ∠ = 5 3 ° and ∠ = 7 18 °, then = _______

d. If = 4 6 and = 12 18, then = _______

W M X

Z N

Y

xq yq

zq

118q

S T

V R

W

A B

C D

F