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Perpendicular Lines 2-5 What are perpendicular lines? • Does it only apply to lines? • From the book: Perpendicular lines are two lines that intersect to form right angles. • Because lines that form one right angle always form four right angles, you can conclude that two lines are perpendicular once you know that any one of the angles they form is a right angle. Remember that a definition is a biconditional. • So… • If two lines are perpendicular, then they form right angles (angles that are 90°). • If two lines form right angles (90°), then the lines are perpendicular. More theorems! YES! Write these- then we’ll prove them • If two lines are perpendicular, then they form congruent, adjacent angles. • If two lines form congruent adjacent angles, then the lines are perpendicular. • If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. If two lines are perpendicular, then they form congruent, adjacent angles. • Given: 𝑙 ⊥ 𝑛 • Prove: ∠1, ∠2, ∠3, ∠4 are congruent angles. If two lines form congruent adjacent angles, then the lines are perpendicular. • Given: ∠1 ≅ ∠2 • Prove: 𝑙 ⊥ 𝑛 If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. • Given: 𝑂𝐴 ⊥ 𝑂𝐶 • Prove: ∠𝐴𝑂𝐵 𝑎𝑛𝑑 ∠𝐵𝑂𝐶 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑎𝑛𝑔𝑙𝑒𝑠.