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Understanding Perpendicular Lines and Their Properties

Perpendicular lines are defined as lines that intersect at a right angle (90 degrees). For example, if line AB intersects line CD at an angle of 90°, we denote this as AB ⊥ CD. The important properties of perpendicular lines include the formation of four right angles when two lines intersect perpendicularly. Additionally, if two angles are formed by two intersecting lines, they are categorized as vertical angles and are congruent. Understanding these concepts is essential in geometry for solving various mathematical problems.

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Understanding Perpendicular Lines and Their Properties

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  1. 3-7 Perpendicular Lines

  2. Lines that intersect at an angle of 90 degrees are perpendicular lines. For example, let’s say that we have the • line AB line CD • and the A Now, if the lines intersect at an angle of 90o, C D then AB  CD. B

  3. Definition of Perpendicular Lines Perpendicular lines are lines that intersect to form a right angle. m Symbols: m  n n

  4. 1 2 4 3 m n

  5. Theorem 3-8 then they form 4 right angles. If two lines are perpendicular, a Symbols: a b 1 2 b 4 3

  6. In the figure, and Determine whether each of the following is true or false. 7 OP MN, OP MN NP QS. QR PR P M False. Since 3 8 1 5 4 3 1 2 2 6 4 R Q True. are vertical angles, and vertical angles are congruent. N O S True. If two lines are perpendicular, then they form 4 right angles. False.

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