Quarterly 2 Test Review. HL Thm SSS Post. AAS Thm

Quarterly 2 Test Review

For #1-5, choose the method used to prove the triangles congruent. HL SAS AAS SSS ASA

1. A and D are right ’s;

HL Thm

2. ;

SSS Post.

3. A and D are right angles;

AAS Thm

4. C is the midpoint of and

SAS Post.

5. bisects ACD;

ASA Post.

6. Complete the following proof by filling in the missing reasons. Given: B C; M is the midpoint of

Prove: STATEMENTS REASONS 1. B C 1. ______________________

2. M is the midpoint of 2.______________________ 3. 3.______________________

4. AMB CMD 4.______________________

5. AMB DMC 5.______________________

6. 6.______________________

GivenGiven

Def. of midpointVertical ’s are .ASA Postulate

CPCTC

7. In an isosceles ABC, is the base and mB = 42°. Find mA and mC.

mA = 96°m = 42°

A

B C42° 42°

8. If two parallel lines are cut by a transversal, then corresponding angles are ____________. 9. If two parallel lines are cut by a transversal, then alternate interior angles are _________. 10. If two parallel lines are cut by a transversal, then same-side interior angles are _____________.

≅

≅

supplementary

11. A median of a triangle is a segment from the vertex to the ________________ of the opposite side.

12. A(n) ___________ of a triangle is a segment from a vertex perpendicular to the opposite side.

13. A perpendicular bisector of a segment is a line (or ray or segment) that is ______________ to the segment as its ______________.

altitude

midpoint

perpendicularmidpoint

For #14-18, answer with always, sometimes, or never.

14. If ΔABC is equiangular, then mB is __________ 65°.

15. In any triangle, there is ______________ at least two acute angles.

16. If two parallel lines are cut by a transversal, then corresponding angles are __________ congruent.

17. If a triangle is isosceles, then it is ____________ right.

18. The acute angles of a right triangle are __________ complementary.

never

always

always

always

sometimes

For #19 and 20, answer with true or false.

19. A triangle may have the sides measuring 12, 28, 40.

20. In right triangle ABC, If mA = 90°, then is the longest side.

FALSE; 12 + 28 = 40

FALSE

A

B

C

21. Find x.

3x + 85 = 8x85 = 5x

x = 17

22. What is the interior angle sum of a decagon? 23. What is the exterior angle sum of a decagon?

24. What is the measure of each interior angle of a regular decagon? 25. What is the measure of each exterior angle of a regular decagon? 26. What polygon has an interior angle measuring 135°?

(n – 2)180 (10 – 2)180 1440°

360°

144°

36°

octagon

int

ext. =

int

27. List the angles from greatest to smallest.

28. List the sides from greatest to smallest.

D, F, E

, , 𝑀𝑁

29. If point O lies in the interior of ABC, then mABC = mABO + m____________.(hint: Draw your own picture.) 30. If point O does not lie on straight angle ABC, then mABO + mCBO = _____°.(hint: Draw your own picture.)

A

B C

O

A B C

O

OBC

180

31. In the diagram, , mDBE = (x – 8)° and mEBC = (3x + 2)°. Find x.

x – 8

3x + 2

x – 8 + 3x + 2 = 904x – 6 = 90

4x = 96

x = 24

For # 32 – 35, name the property is used. 32. If a = b and b = c, then a = c. 33. If a = b, then b = a. 34. a = a 35. If a = b and a + c = d, then b + c = d.

Transitive Property

Symmetric Property

Reflexive Property

Substitution Property

36. If two lines intersect, then their intersection is a ______________. 37. If two planes intersect, then their intersection is a ______________.

point

line

38. If mROS = (6x + 3)° and mTOP = (8x - 7)°, then x = ____.

6x + 3

8x - 7

8x – 7 = 6x + 3

x = 5

5

39. X is the midpoint of . If WX = (3x), XZ = (x + 6), then find x.

3x x + 6

3x = x + 62x = 6

x = 3

For #40 - 46, a || b and m1 = 75°.

40. 1 and 5 are _______________ angles.

41. 2 and 6 are _______________ angles. 42. 5 and 6 are _______________ angles.

43. m2 = ________44. m3 = ________

45. m5 = ________

corresponding

s-s interior

alt. interior

105°

105°

75°

75°

46. m5 = (6x + 2)° and m6 = (8x – 10)°. Find x.

6x + 2 = 8x – 10 12 = 2x

x = 6

47. What is the image of P(3, –5) using the translation (x, y) → (x + 4, y – 6)?

P’(7, –11)

P’(3 + 4, –5 – 6)

For #48-51, use the coordinate plane to the right.48. What is the image of P(1, 4) if (x, y) is reflected in the y–axis? 49. What is the image of P(1, 4) if (x, y) is reflected in the x-axis?

P’(–1, 4)

P’(1, –4)

50. What is the image of P(1, 4) if (x, y) is reflected in the line y = x?

51. What is the image of P(1, 4) if (x, y) is reflected in the line y = –x?

P’(4, 1)

P’(–4, –1)

For #52 – 54, describe the transformation shown.52.

translation (x, y) (x + 2, y – 8)

53.

reflection over x-axis

54.

rotation 180° clockwise or counterclockwise

about the origin

STUDY