1. Proving things about Angles
Chapter 2 Section 2.6-Part 2
Proving things about Angles

2. Properties of Angle Congruence
Angle congruence is reflexive, symmetric, and transitive
Reflexive:
Symmetric:
Transitive:

3. More Theorems and Postulates
Theorem 2.3 Right Angle Congruence Theorem
All right angles are congruent A B
A and B are both right angles. Thus, A  B

4. More Theorems and Postulates
Theorem 2.4 Congruent supplements theorem
If two angles are supplementary to the same angle, then they are congruent to each other H G
138°
42° P
G and P are supplementary.
H and P are supplementary.
Thus, G  H

5. More Theorems and Postulates
Theorem 2.5 Congruent complements theorem
If two angles are complementary to the same angle, then they are congruent to each other
60° M
30° N Q
N and M are complementary.
Q and M are complementary.
Thus, N  Q

6. More Theorems and Postulates
Postulate 12 Linear Pair Postulate
If two angles form a linear pair, then they are supplementary
Theorem 2.6 Vertical Angle Theorem
Vertical Angles are congruent

7. Complete the statement given that mBHD = mCHE = mEHF = 90°
If m3 = 42, then m6 = _____ 42
If mBHE = 142, then m1 = _____ 52
If m1 = 37, then m6 = _____ 37
If mEHG = 132, then m7 = _____
If m7 = 51, then m3 = _____ 39
If mEHB = 153, then m2 = _____ 27 1 2 3 4 5 6 7
• A
• B
• C
• D
• E
• F H
• G

8. Write a Two Column Proof
Given: 1 and 2 are Supplementary
3 and 2 are Supplementary
Prove: 1  3
Statements Reasons
1 and 2 are Supplementary
3 and 2 are Supplementary
1. Given
2. m1 + m2 = m3 + m2 = 180
2. Def. Supp. Angles
3. m1 + m2 = m3 + m2
3. Substitution
4. m1 = m3
4. Subtraction
5. 1  3
5. Def. Congruent Angles

9. Given: 1 and 2 are complementary 1  3 and 2  4
Prove: 3 and 4 are complementary
Statements Reasons
1. Given
1. 1 and 2 are complementary
1  3 and 2  4
2. m1 + m2 = 90
2. Def. of Complementary Angles
3. m1 = m3, m2 = m4
3. Def.  Angles
4. m3 + m2 = 90
4. Substitution
5. m3 + m4 = 90
5. Substitution
6. 3 and 4 are complementary
6. Def. of Complementary Angles