Sec. 3-3 Parallel and Perpendicular Lines

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

Th(3-9) If two lines are // to the same line, then they are // to each other. 1 2 k 3 4 5 6 m 7 8 9 10 n 11 12

Th(3-9) If two lines are // to the same line, then they are // to each other. k 5 6 m 7 8 9 10 n 11 12

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

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

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

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

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