1. Prove Theorems About Perpendicular Lines
Section 3 – 6
Prove Theorems About Perpendicular Lines

2. Theorem 3.8
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
If 1 = 2, then g h. g 1 2 h

3. Theorem 3.9
If two lines are perpendicular, then they intersect to form four right angles.
If a b, then 1, 2, 3, & 4 are right angles. b 1 2 a 3 4

4. Theorem 3.10
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
If BA BC, then and 2 are complementary. A 1 2 B C

5. Theorem 3.11
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
If h k and j h, then j k. j h k

6. Theorem 3.12
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
If m p and n p, then m n. m n p

7. Example 1 Explain how you would show that m || n . First: Find x:
Since x° and x° form a linear pair we can say:
x ° = 90 ° by Theorem 3.8
Therefore
Second:
If and then by
Theorem 3.11

8. Example 2 2x – 9 + x = 90 3x – 9 = 90 +9 +9 3x = 99 3 3 x = 33
In the diagram, Find the value of x
2x – 9 + x = 90
3x – 9 = 90
3x = 99
x = 33

9. Example 2 Prove that if 1 and 2 are complementary, then BA BC. ˜
Given: 1 & 2 are comp.
Prove: BA BC. C D 2 1 A B
Statement Reasons
& 2 are comp.
Given
Def. of comp. ‘s
2. m m = 90◦
3. m ABC = m m 2
Angle Add. Post.
Subst. Prop. of =
4. m ABC = 90◦
ABC is a rt.
Def. of rt.
6. BA BC
Def. of lines

10. Homework
Section 3-6
Page 194 – 197
5 – 11, 15 – 19,
21, 26,