Using the diagram below complete these sentences 1

Using the diagram below, complete these sentences: 1. _______ are always _______. 2. _______ are sometimes ________. 3. _______ are never _______. birds four-footed mammals dogs poodles

Mod 14. 3: Proving Lines are Parallel Essential Question: How can you prove that two lines are parallel? CASS: G-CO. 9 Prove theorems about lines and angles. MP. 3 Logic

Conditional Statements Venn Diagram Conclusion “q” Hypothesis “p” • Read “if p then q” • Symbols: p q Example: If parallel lines are cut by a transversal, then its alternate int. angles are congruent. Conclusion “alt. int. angles congruent” Hypothesis “parallel lines°”

Converse • Converse of a conditional statement is formed by switching the hypothesis and conclusion. • Conditional Statements: if “p” then “q” • Converse: if “q” then “p”

Write the converse of the conditional statement Conditional Statement (p q): If parallel lines are cut by a transversal, then its alternate interior angles are congruent. Converse (q p): If alternate interior angles are congruent, then the lines are parallel.

SAME SIDE INTERIOR ANGLES CONVERSE POSTULATE If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. 2 1 If , then j ‖ k.

CORRESPONDING ANGLES CONVERSE THEOREM If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. j‖k

ALTERNATE INTERIOR ANGLES CONVERSE THEOREM If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 3 1 If , then j ‖ k ALTERNATE EXTERIOR ANGLES CONVERSE THEOREM If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. 1 8 If , then j ‖ k

EXAMPLE 1 Find the value of x that make m || n. m n Alt. Int. Angles Converse

TRY THIS a b Find the value of x that makes a || b. Cons. Int. Angles Converse

14. 3 key question: How can we prove two lines are parallel?

ASSIGNMENTS • pp. 705 #1, 3, 5 -10 all Key Vocab: ü ü ü Parallel Lines Transversal Same Side Interior Angles Converse Corresponding Angles Converse Alternate Interior Angles Converse

TICKET-OUT-THE-DOOR Suppose m∠ 6 = 83°. Find measure of all the other angles. 1 2 4 3 7 8 6 5 What is the relationship between angles 1 and 7? What is the relationship between angles 4 and 8? What is the relationship between angles 3 and 8?