Entry Task Given: =180 Prove: L // m L m

Parallel and Perpendicular Lines 3.4 Learning Target: I can make a conjecture that relates //,and lines and there transversals. Success Criteria: I can relate 2 // lines to a third line and decide if the 3 rd line is // or

On your own….. 1.Draw // lines and label then a and b 2.Draw a line and label it c but make sure it is // to line a only and not line b 3.What do you notice? Is it always true? Why? Next 1.Draw line m perpendicular to t and n perpendicular to t as well. 2.What can you tell me about m and n? Is it always true? Why?

Finally 1.Draw n perpendicular to L and L // to m 2.What can you tell me about n and m?

Example 1: Carpentry Application A carpenter’s square forms a right angle. A carpenter places the square so that one side is parallel to an edge of a board, and then draws a line along the other side of the square. Then he slides the square to the right and draws a second line. Why must the two lines be parallel? Both lines are perpendicular to the edge of the board. If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other, so the lines must be parallel to each other.

Example 2: Proving Properties of Lines Write a two-column proof. Given: r || s, 1  2 Prove: r  t

Example 2 Continued StatementsReasons 2. 2  3 3. 1  3 3. Trans. Prop. of  2. Corr. s Post. 1. r || s, 1  2 1. Given 4. r  t 4. 2 intersecting lines form lin. pair of  s  lines .

Homework Homework: P. 168 #6,7,11-15,19-24,27,29, Challenge – 26

Check It Out! Example 3 Write a two-column proof. Given: Prove:

Check It Out! Example 3 Continued StatementsReasons 3. Given 2. Conv. of Alt. Int. s Thm. 1.  EHF  HFG 1. Given 4.  Transv. Thm

Lesson Quiz 1. Complete the two-column proof below. Given: 1 ≅ 2, p  q Prove: p  r Proof StatementsReasons 1. 1 ≅ 2 1. Given 2. q || r 3. p  q 4. p  r 2. Conv. Of Corr. s Post. 3. Given 4.  Transv. Thm.