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Sec. 3-3 Parallel and Perpendicular Lines Objective: To relate Parallel & Perpendicular Lines.

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Th(3-9) If two lines are // to the same line, then they are // to each other. k m n 12 34 56 78 910 11 12 t

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k m n 56 78 910 11 12 t

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Th(3-10) In a plane, if 2 lines are perpendicular to the same line, then they are // to each other. r s t

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Th(3-11) In a plane, if a line is perpendicular to one of two parallel lines, then it is parallel to the other. r s t

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r s t Corresponding Angles are Corresponding Angles are They are = 90 Alt. Int. s are Alt. Int. s are They are = 90 Same-sided int. s are Supplementary They are both = 90

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Example 1: Solve for x and then solve for each angle such that n // m. 14 + 3x 5x - 66 n m 14 + 3x = 5x -66 -3x -3x 14 = 2x – 66 +66 80 = 2x 2 40 = x 14 + 3x 14 + 3(40) = 134 5x – 66 5(40) – 66 134

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Example 2: Find the m 1 62 7x - 8 7x – 8 + 62 = 180 7x + 54 = 180 7x = 126 x = 18 1 7x – 8 7(18) – 8 118

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