2 8 Proving Angle Relationships Part II 1 of 2

2 ? 8 Proving Angle Relationships ? Part II 1 of 2

Vertical Angles Theorem: Vertical Angles are Congruent.

3 4

3 4

1. Prove the Vertical Angle Theorem

Given: 1 and 2 are Vertical Angles Prove: m1 = m2

Statements

Reasons

1. 1 & 2 are Vert. 's 1. Given

1 2 3

2. m1 + m2 = 180?

2. Def. Supplementary 's

m1 + m3 = 180?

3. m1 + m2 = m1 + m3 3. Substitution

4. m1 = m2

4. Subtraction Prop. =

2 ? 8 Proving Angle Relationships ? Part II 2 of 2

Right Angle Theorems

2.9 Perpendicular lines form

four right angles.

1 2

3 4 Ex. 1, 2, 3, & 4 are Right 's.

2.10 All right angles are Congruent.

Ex. 1 2 3 4

2.11 Perpendicular lines form congruent adjacent angles.

Ex. 1 2 1 3 3 4 2 4

2.12 If two angles are congruent and supplementary, then each angle is a right angle.

2.13 If two congruent angles form

a linear pair, then they are

right angles.

5 6

Ex. 5 6, and 5 & 6 are Right 's

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