4-7 Vertical Angles

Vertical angle definition

• Two angles are vertical angles if their sides form two pairs of opposite rays.• 1 and 2 are vertical angles

Vertical angle theorem• Vertical angles are congruent• Create a sketch

• Write the given and the prove• Given: 1 and 2 are a vertical angles• Prove: 1 2

Vertical angle theorem• Vertical angles are congruent

Statements Reasons

1. 1 and 2 are vertical angles Given

2. Def of vertical angles

3. 1 and 3 form a linear pair2 and 3 form a linear pair

Def of linear pair

4. 1 is supplementary to 3 2 is supplementary to 3

Supplement Postulate

5. 3 3 Reflexive prop

6. 1 2 Supplement Theorem

raysoppositeareADandAB

raysoppositeareAEandAC

Q.E.D.

Perpendicular Lines theorem

• If 2 lines are perpendicular they form four right angles• Create a sketch

• Write the given and the prove• Given: L1 L2

• Prove: 1, 2, 3, 4 are right angles

12

3 4

L2

L1

Perpendicular Lines theorem• If 2 lines are perpendicular they form four right angles

Statements Reasons

1. L1 L2 Given

2. 1 is a right angle Def of perpendicular

3. m1 = 90 Def. of right angle

4. 1 and 2 are a linear pair Given sketch

5. 1 and 2 are a supplementary Supplement Postulate

6. m1 + m2 = 180 Def of suppl.

7. 90 + m2 = 180 Substitution 2 into 6

8. m2 = 90 Subtraction prop. of eq.

9. m3 = 90 Vertical Angle Theorem

10. m4 = m90 Vertical Angle Theorem Q.E.D.

Homework

• Pg. 106 – 108: #2 - 10. In 10, note that the problem is discussing two situations.• Pg. 109 #1, 2