birds four-footed mammals dogs poodles Using the diagram below, complete these sentences: _____________ are always ______________. ______________ are sometimes ________________. _____________ are never ______________. birds four-footed mammals dogs poodles

Proving Lines are Parallel 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 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 “q” Hypothesis “p” 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. If , 1 2 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. If , then j ‖ k 1 3 ALTERNATE EXTERIOR ANGLES CONVERSE THEOREM 1 8 If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. If , then j ‖ k

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

Find the value of x that makes a || b. 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?

pp. 705 #1, 3, 5-10 all Key Vocab: ASSIGNMENTS 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?