Chapter 2Section 2.6-Part 2

Proving things about Angles

Properties of Angle Congruence

• Angle congruence is reflexive, symmetric, and transitive

Reflexive: AAAangleanyFor ,

Symmetric: ABthenBAIf ,

Transitive: CAthenCBandBAIf

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

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

H42°

PG138°

G and P are supplementary.

H and P are supplementary.

Thus, G H

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°

M30°

NQ

N and M are complementary.

Q and M are complementary.

Thus, N Q

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

Complete the statement given that mBHD = mCHE = mEHF = 90°

•If m3 = 42, then m6 = _____

•42

•If mBHE = 142, then m1 = _____

•52

•If m1 = 37, then m6 = _____

•37

•If mEHG = 132, then m7 = _____

•42

•If m7 = 51, then m3 = _____

•39

•If mEHB = 153, then m2 = _____

•27

12 3

4

56

7

• A• B

• C

• D• E

• F

H

• G

1. Given

2. Def. Supp. Angles

3. Substitution

Write a Two Column Proof

Statements Reasons

1. 1 and 2 are Supplementary

3 and 2 are Supplementary

2. m1 + m2 = 180 m3 + m2 = 180 3. m1 + m2 = m3 + m2

4. m1 = m3 4. Subtraction

Given: 1 and 2 are Supplementary

3 and 2 are Supplementary

Prove: 1 3

5. 1 3 5. Def. Congruent Angles

Given: 1 and 2 are complementary

1 3 and 2 4

Prove: 3 and 4 are complementary

3. Def. Angles

1. Given

2. Def. of Complementary Angles

4. Substitution

6. Def. of Complementary Angles

1

23

4

Statements Reasons

1. 1 and 2 are complementary

1 3 and 2 42. m1 + m2 = 903. m1 = m3, m2 = m44. m3 + m2 = 905. m3 + m4 = 90 5. Substitution6. 3 and 4 are complementary