Proving Lines Parallel Section 3.5 Proving Lines Parallel

Converse Switching the hypothesis and the conclusion of a statement to make another statement, called the converse. Usually “If, then” statements.

Converse of Corresponding Angles Postulate If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. If ⦟1≅⦟3, ⦟2≅⦟4, ⦟5≅⦟7, ⦟6≅⦟8, then a||b

Parallel Postulate Given a line and a point not on a line, then there exists exactly one line through the point that is parallel to the given line.

Alternate Exterior Angles Converse If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

Consecutive Interior Angles Converse If two lines are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the two lines are parallel.

Alternate Interior Angles Converse If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

Perpendicular Transversal Theorem If two lines are perpendicular to the same line, then they are parallel.

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Example 1: Use the diagram to the right. a) Given Ð1 @ Ð3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.

Example 1: Use the diagram to the right. b) Given mÐ1 = 103 and mÐ4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.

Example 2 Given Ð1 @ Ð5, is it possible to prove that any of the lines shown are parallel?

Example 3 a) Find mÐZYN so that PQ|| MN . Show your work.

Example 3 b) Find x so that GH||RS .

Example 4 In the window shown, the diamond grid pattern is constructed by hand. Is it possible to ensure that the wood pieces that run the same direction are parallel? If so, explain how. If not, explain why not.

Example 5 In the game Tic-Tac-Toe, four lines intersect to form a square with four right angles in the middle of the grid. Is it possible to prove any of the lines parallel or perpendicular? Choose the best answer. a) The two horizontal lines are parallel. b) The two vertical lines are parallel. c) The vertical lines are perpendicular to the horizontal lines. d) All of these statements are true.