3.2 Proof and Perpendicular Lines

Let’s Review

Theorem 2.6-Vertical Angles Theorem• Vertical angles are

congruent….• Given: <5 & <6 are a linear

pair; <6 & <7 are a linear pair.

• Prove: m<5=m<7

76

5

Statement Reason1. <5 & <6, <6 &<7 are a linear pair

1. Given

2. <5 & <6, <6 & <7 are supplements

2. Linear Pair Postulate

3. m<5=m<7 3. Congruent Supplements Theorem

Theorem 3.1 (p137)

• If two lines intersect to form a linear pair of congruent angles,

• Then the lines are perpendicular.

gh

h

g

Theorem 3.2

• If two sides of two adjacent acute angles are perpendicular,

• Then the angles are complementary.

Theorem 3.3

• If two lines are perpendicular,

• Then they intersect to form four right angles. 90

90

90

90

State the Reason for the Conclusion:

State the Reason for the Conclusion:

State the Reason for the Conclusion:

State the Reason for the Conclusion:

State the Reason for the Conclusion:

Find the value of x:

Find the value of x:

Find the value of x: