1. 3.5 Using Properties of Parallel Lines

2. Example 1: Proving Two Lines are Parallel
Goal 1: Using Parallel Lines in Real Life
Example 1: Proving Two Lines are Parallel
Lines m, n and k represent three of the oars of a team of rowers.
Given: m║n and n║k. Prove: m║k. 1 m 2 n 3 k

3. Proof Statements: m║n 1 ≅ 2 n║k 2 ≅ 3 1 ≅ 3 m║k Reasons: Given
Corresponding Angles Postulate
Transitive POC
Corresponding Angles Converse

4. Parallel/Perpendicular lines Theorems
Theorem 3.11: If two lines are parallel to the same line, then they are parallel to each other. r q p
If p║q and q║r, then p║r.

5. Parallel/Perpendicular lines Theorems
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

6. Example 2: Why Steps are Parallel
In the diagram at the right, each step is parallel to the step immediately below it and the bottom step is parallel to the floor. Explain why the top step is parallel to the floor. k1 k2 k3 k4

7. Example 2: Why Steps are Parallel (cont.)
Solution
You are given that k1║ k2 and k2║ k3. By transitivity of parallel lines, k1║ k3. Since k1║ k3 and k3║ k4, it follows that k1║ k4. So the top step is parallel to the floor. k1 k2 k3 k4

8. Example 3: Building a CD Rack
You are building a CD rack. You cut the sides, bottom, and top so that each corner is composed of two 45° angles. Prove that the top and bottom front edges of the CD rack are parallel.

9. Proof Given: m1 = 45°, m2 = 45°, m3 = 45°, m = 45° Prove: BA║CD B

10. BCCD BABC BA║CD m3=45°, m4=45° m1=45°, m2=45° mABC = 90°
mBCD = m3+ m4
mABC = m1+ m2
Angle Addition Postulate
Given
Angle Addition Postulate
Given
mABC = 90°
mBCD = 90°
Substitution Property
Substitution Property
ABC is a right angle.
BCD is a right angle.
Definition of Right Angle
Definition of Right Angle
BCCD
BABC
Definition of  lines
Definition of  lines
BA║CD
In a plane, 2 lines to the same line are ║.