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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