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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.