1. 3.2 Proof and Perpendicular Lines

2. Let’s Review

3. 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
Statement
Reason
1. <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

4. Theorem 3.1 (p137)
If two lines intersect to form a linear pair of congruent angles,
Then the lines are perpendicular.

5. Theorem 3.2
If two sides of two adjacent acute angles are perpendicular,
Then the angles are complementary.

6. Theorem 3.3 If two lines are perpendicular,
Then they intersect to form four right angles.

7. State the Reason for the Conclusion:

8. State the Reason for the Conclusion:

9. State the Reason for the Conclusion:

10. State the Reason for the Conclusion:

11. State the Reason for the Conclusion:

12. Find the value of x:

13. Find the value of x:

14. Find the value of x: