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9-2 Parallel and Perpendicular Lines Parallel lines are lines in a plane that never meet. Perpendicular lines are lines that intersect at 90° angles. 9-2 Parallel and Perpendicular Lines The sides of the windows are transversals to the top and bottom. The top and bottom of the windows are parallel. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties. 9-2 Parallel and Perpendicular Lines Caution! You cannot tell if angles are congruent by measuring because measurement is not exact. 9-2 Parallel and Perpendicular Lines Additional Example 1: Identifying Congruent Angles Formed by a Transversal Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 9-2 Parallel and Perpendicular Lines Additional Example 1 Continued Angles circled in blue appear to be congruent to each other, and angles circled in red appear to be congruent to each other. ∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7 ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8 9-2 Parallel and Perpendicular Lines Check It Out: Example 1 Measure the angles formed by the transversal and the parallel lines. Which angles appear to be congruent? 1 2 3 4 5 6 7 8 ∠1, ∠4, ∠5, and ∠8 all measure 36° and appear congruent. ∠ 2, ∠3, ∠6, and ∠7 all measure 144° and appear congruent. 9-2 Parallel and Perpendicular Lines Some pairs of the eight angles formed by two parallel lines and a transversal have special names. 9-2 Parallel and Perpendicular Lines 9-2 Parallel and Perpendicular Lines Writing Math The symbol for parallel is ||. The symbol for perpendicular is ⊥. 9-2 Parallel and Perpendicular Lines Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued In the figure, line l || line m. Find the measure of the angle. ∠2 ∠6 ∠4 9-2 Parallel and Perpendicular Lines Check It Out: Example 2A In the figure, line n || line m. Find the measure of each angle. Justify your answer. 1 144° m ∠5 3 4 5 6 n 7 8 ∠7 ∠8 ∠6