1. Section 2.8 ~ Proving Angles Relationships
Be able to apply theorems to prove angles congruent!
Given: AB = BC A B C

6. Solve for x. Fill in each missing reason:
Given: LM bisects KLN M N
LM bisects KLN
mNLM = mMLK
4x = 2x + 40
2x = 40
x = 20
given L K
def  bisector
substitution
subtraction
division

7. Solve for x and justify each step:B
Given: mAXC = 139° A
mAXC = 139
mAXB + mBXC = mAXC
x + 2x + 10 = 139
3x + 10 = 139
3x = 129
x = 43
given X C
 addition postulate
substitution
simplify
subtraction
division

8. Try it on your own! Find the value of x and justify each step.
4x = 2x + 3
_________
________
subtraction
2x = 104
_________
________
division

9. Using the Transitive Property of Angle Congruence
Statement:
A ≅ B, B ≅ C
mA = mB
mB = mC
mA = mC
A ≅ C
Reason:
Given
Def. Cong. Angles
Transitive property of equality

10. Using the Transitive Property
Given: m3 = 40, 1 ≅ 2, 2 ≅ 3 Prove: m1 = 40 1 4 2 3

11. Using the Transitive Property
Statement:
m3 = 40, 1 ≅ 2, 2 ≅ 3
1 ≅ 3
m1 = m 3
m1 = 40
Reason:
Given
Trans. Prop of Cong. Angles
Def. Cong. Angles
Substitution

12. Proving All rt <‘s are congruent
Reason:
Given
Def. Right angle
Transitive property
Def. Cong. Angles
Statement:
1 and 2 are right angles
m1 = 90, m2 = 90
m1 = m2
1 ≅ 2

13. Proving Complement/Supplement Theorem
Given: 1 and 2 are supplements, 3 and 4 are supplements, 1 ≅ 4 Prove: 2 ≅ 3 3 4 1 2

14. Proving complement/Supplement Theorem
Reason:
Given
Def. Supplementary angles
Transitive property of equality
Def. Congruent Angles
Substitution property
Subtraction property
Statement:
1 and 2 are supplements, 3 and 4 are supplements, 1 ≅ 4
m 1 + m 2 = 180; m 3 + m 4 = 180
m 1 + m 2 =m 3 + m 4
m 1 = m 4
m 1 + m 2 =m 3 + m 1
m 2 =m 3
2 ≅ 3

15. Using Linear Pairs
In the diagram, m8 = m5 and m5 = 125. Explain how to show m7 = 55 7 8 5 6

16. Solution:
Using the transitive property of equality m8 = 125. The diagram shows that m 7 + m 8 = 180. Substitute 125 for m 8 to show m 7 = 55.

17. Proving The Vertical Angles Theorem
Given: 5 and 6 are a linear pair, 6 and 7 are a linear pair Prove: 5 7 5 7 6

18. Proving the Vertical Angles Theorem
Statement:
5 and 6 are a linear pair, 6 and 7 are a linear pair
5 and 6 are supplementary, 6 and 7 are supplementary
5 ≅ 7
Reason:
Given
Linear Pair postulate
Congruent Supplements Theorem