1. Using Segment and Angle Addition Postulates
More Proofs
Using Segment and Angle Addition Postulates

2. State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO
A. Distributive Property
B. Addition Property
C. Substitution Property
D. Multiplication Property

3. State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO
A. Distributive Property
B. Addition Property
C. Substitution Property
D. Multiplication Property

4. State the property that justifies the statement. If 2PQ = OQ, then PQ =
A. Multiplication Property
B. Division Property
C. Distributive Property
D. Substitution Property

5. State the property that justifies the statement. If 2PQ = OQ, then PQ =
A. Multiplication Property
B. Division Property
C. Distributive Property
D. Substitution Property

6. State the property that justifies the statement. mZ = mZ
A. Reflexive Property
B. Symmetric Property
C. Transitive Property
D. Substitution Property

7. State the property that justifies the statement. mZ = mZ
A. Reflexive Property
B. Symmetric Property
C. Transitive Property
D. Substitution Property

8. State the property that justifies the statement
State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF.
A. Reflexive Property
B. Symmetric Property
C. Substitution Property
D. Transitive Property

9. State the property that justifies the statement
State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF.
A. Reflexive Property
B. Symmetric Property
C. Substitution Property
D. Transitive Property

10. Which statement shows an example of the Symmetric Property?
A. x = x
B. If x = 3, then x + 4 = 7.
C. If x = 3, then 3 = x.
D. If x = 3 and x = y, then y = 3.

11. Which statement shows an example of the Symmetric Property?
A. x = x
B. If x = 3, then x + 4 = 7.
C. If x = 3, then 3 = x.
D. If x = 3 and x = y, then y = 3.

12. 2. Definition of congruent segments AB = CD 2.
Proof:
Statements Reasons 1.
1. Given
AB  CD
___
2. Definition of congruent segments
AB = CD 2.
3. Reflexive Property of Equality
BC = BC 3.
4. Segment Addition Postulate
AB + BC = AC 4.

13. 5. Substitution Property of Equality 5. CD + BC = AC
Proof:
Statements Reasons
5. Substitution Property of Equality
5. CD + BC = AC
6. Segment Addition Postulate
CD + BC = BD 6.
7. Transitive Property of Equality
AC = BD 7.
8. Definition of congruent segments 8.
AC  BD
___

14. Prove the following.
Given: AC = AB AB = BX CY = XD
Prove: AY = BD

15. 1. Given
AC = AB, AB = BX 1.
2. Transitive Property
AC = BX 2.
3. Given
CY = XD 3.
4. Addition Property
AC + CY = BX + XD 4.
AY = BD
6. Substitution 6.
Proof:
Statements Reasons
Which reason correctly completes the proof?
5. ________________
AC + CY = AY; BX + XD = BD 5. ?

16. A. Addition Property
B. Substitution
C. Definition of congruent segments
D. Segment Addition Postulate

17. A. Addition Property
B. Substitution
C. Definition of congruent segments
D. Segment Addition Postulate

18. Jamie is designing a badge for her club
Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge.
Given:
Prove:

19. 2. Definition of congruent segments 2.
Proof:
Statements Reasons
1. Given 1.
2. Definition of congruent segments 2.
3. Given 3.
4. Transitive Property 4. YZ
___
5. Substitution 5.

20. Which choice correctly completes the proof?
Statements Reasons
1. Given 1.
2. Transitive Property 2.
3. Given 3.
4. Transitive Property 4.
5. _______________ 5. ?

21. A. Substitution
B. Symmetric Property
C. Segment Addition Postulate
D. Reflexive Property

22. A. Substitution
B. Symmetric Property
C. Segment Addition Postulate
D. Reflexive Property

23. Justify the statement with a property of equality or a property of congruence.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

24. Justify the statement with a property of equality or a property of congruence.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

25. Justify the statement with a property of equality or a property of congruence.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

26. Justify the statement with a property of equality or a property of congruence.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

27. Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

28. Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI.
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Segment Addition Postulate

29. State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate.
A. WX > WZ
B. XW + WZ = XZ
C. XW + XZ = WZ
D. WZ – XZ = XW

30. State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate.
A. WX > WZ
B. XW + WZ = XZ
C. XW + XZ = WZ
D. WZ – XZ = XW

31. State a conclusion that can be drawn from the statements given using the property indicated.
LM  NO
___ A. B. C. D.

32. State a conclusion that can be drawn from the statements given using the property indicated.
LM  NO
___ A. B. C. D.

33. Given B is the midpoint of AC, which of the following is true?
___
A. AB + BC = AC
B. AB + AC = BC
C. AB = 2AC
D. BC = 2AB

34. Given B is the midpoint of AC, which of the following is true?
___
A. AB + BC = AC
B. AB + AC = BC
C. AB = 2AC
D. BC = 2AB

35. A construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?
The ceiling and the wall make a 90 angle. Let 1 be the angle between the beam and the ceiling. Let 2 be the angle between the beam and the wall.
m1 + m2 = 90 Angle Addition Postulate
42 + m2 = 90 m1 = 42
42 – 42 + m2 = 90 – 42 Subtraction Property of Equality
m2 = 48 Substitution

36. Answer:

37. Answer: The beam makes a 48° angle with the wall.

38. Find m1 if m2 = 58 and mJKL = 162.
B. 94
C. 104
D. 116

39. Find m1 if m2 = 58 and mJKL = 162.
B. 94
C. 104
D. 116

40. At 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?
Understand Make a sketch of the situation. The time is 4 o’clock and the second hand bisects the angle between the hour and minute hands.

41. Plan Use the Angle Addition Postulate and the definition of angle bisector.
Solve Since the angles are congruent by the definition of angle bisector, each angle is 60°.
Answer:

42. Plan Use the Angle Addition Postulate and the definition of angle bisector.
Solve Since the angles are congruent by the definition of angle bisector, each angle is 60°.
Answer: Both angles are 60°.
Check Use the Angle Addition Postulate to check your answer.
m1 + m2 = 120
= 120
120 = 120 

43. The diagram shows one square for a particular quilt pattern
The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.
A. 20
B. 30
C. 40
D. 50

44. QUILTING The diagram shows one square for a particular quilt pattern
QUILTING The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.
A. 20
B. 30
C. 40
D. 50

45. Example 3
Given:
Prove:

46. Proof:
Statements Reasons
1. Given
1. m3 + m1 = 180; 1 and 4 form a linear pair.
2. Linear pairs are supplementary.
2. 1 and 4 are supplementary.
3. Definition of supplementary angles
3. 3 and 1 are supplementary.
4. s suppl. to same  are .
4. 3  4

47. In the figure, NYR and RYA form a linear pair, AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that NYR and AXY are congruent.

48. Which choice correctly completes the proof? Proof:
Statements Reasons
1. Given
1. NYR and RYA, AXY and AXZ form linear pairs.
2. If two s form a linear pair, then they are suppl. s.
2. NYR and RYA are supplementary. AXY and AXZ are supplementary.
3. Given
3. RYA  AXZ
4. NYR  AXY
4. ____________ ?

49. A. Substitution
B. Definition of linear pair
C. s supp. to the same  or to  s are .
D. Definition of supplementary s

50. A. Substitution
B. Definition of linear pair
C. s supp. to the same  or to  s are .
D. Definition of supplementary s

51. 2. Vertical Angles Theorem
If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.
Statements Reasons
Proof:
1. 1 and 2 are vertical s.
1. Given
2. 1  2
2. Vertical Angles Theorem
3. m1 = m2
3. Definition of congruent angles
4. d – 32 = 175 – 2d
4. Substitution

52. Statements Reasons 5. Addition Property 6. Addition Property
7. Division Property
m1 = d – 32 m2 = 175 – 2d
= 69 – 32 or 37 = 175 – 2(69) or 37
Answer:

53. Statements Reasons 5. Addition Property 6. Addition Property
7. Division Property
m1 = d – 32 m2 = 175 – 2d
= 69 – 32 or 37 = 175 – 2(69) or 37
Answer: m1 = 37 and m2 = 37

54. A. B. C. D.

55. A. B. C. D.