Bellwork 1. Solve for x. 2. Construct a line perpendicular to line s that passes through H. H

Lesson 3-3 & 3-4: Parallel & Perpendicular Line Proofs Rigor – Prove lines are parallel or perpendicular; determine the value of x that will make lines parallel Relevance – logical thinking, construction

Recap: Theorems vs Converses The angle pair THEOREMS: Given - lines are parallel Conclusion – angle pairs are or supplementary Angle pair CONVERSES: Given - angle pairs are or supplementary Conclusion – lines are parallel

Example 1: Which lines are parallel? Justify your answer.  

Example 2: Applying the Converse What value of x would make the lines parallel? a) b)

Example 3: Rowing Application  

Theorems to know: Perpendicular Transversal Theorem If a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other line. Corollary to the Corresponding Angles Converse – If 2 coplanar lines are perpendicular to the same line, then they are parallel to each other.

Theorems to know continued:  

Example 4  

Distance from a Point to a Line  

Proof of the ⊥ Transversal Theorem   Reasons ________________ Definition of congruent _________________  

Example 5: Proof   Reasons ________________ Given _________________  

3-3 and 3-4 Classwork: Heading: 3-3 &3-4 CW from the textbook Page 166 – 167 #10, 11, 23, 27 – 32 Page 176 #9, 12 – 14, 16 – 22 Whatever you don’t finish in class is homework. Due Monday for periods 1, 3, 5, & 7 Due Tuesday for periods 2 & 4