1. Do Now

2. 3.6: Prove Theorems about Perpendicular Lines
Geometry
3.6: Prove Theorems about Perpendicular Lines

3. Theorems
Theorem 3.8: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Theorem 3.9: If two lines are perpendicular, then they intersect to form 4 right angles. 1 2 1 2 3 4

4. Theorems
Theorem 3.10: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 1 2

5. Theorems
Theorem 3.11: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Theorem 3.12: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

6. p.195 #15 and 17: Solve for x.
15.)
17.) 63
x+14
2x–9 x

7. Use the diagram below. r s t
1.) Is r s?
2.) Is m n?
3.) Is r t? m n

8. Homework
Study Guide for Section 3.6

9. Chapter 3 Test (3.1-3.6) 3.1: Vocabulary 3.2: Parallel Lines
Parallel, skew, perpendicular
Alt. Int, Alt. Ext, Corresponding, Consec. Int.
3.2: Parallel Lines
Alt. Int. angles, Alt. Ext. angles, and Corresponding angles are congruent.
Consec. Int. angles are supplementary.
3.3: Determine if lines are parallel
Converse of theorems

10. Chapter 3 Test ( )
3.4: Slope- Determine if lines are parallel, perpendicular, or neither.
Parallel lines: same slope
Perpendicular lines: slopes are negative reciprocals
3.5: Lines
Graphing
Write equation of lines using either:
y = mx + b
y – y1 = m(x – x1)
Write equations of lines parallel or perp. to other lines given graph or equation.

11. Chapter 3 Test (3.1-3.6) 3.6: Perpendicular Lines Theorems
Identify if lines are parallel given information.
Solve for x