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5-2. Parallel and Perpendicular Lines. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 5-2. Parallel and Perpendicular Lines. Pre-Algebra. Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ .

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5-2

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  1. 5-2 Parallel and Perpendicular Lines Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  2. 5-2 Parallel and Perpendicular Lines Pre-Algebra Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . 2. Vertical angles have equal measures, so they are ______________. 3. Angles whose measures have a sum of 180° are ______________. 4. A part of a line between two points is called a ____________. complementary congruent supplementary segment

  3. I will be able to identify parallel and perpendicular lines and the angles formed by a transversal and solve real-world problems .

  4. Vocabulary parallel lines perpendicular lines transversal

  5. Parallel lines are two lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. Perpendicular lines are lines that intersect to form 90° angles.

  6. The railroad ties are transversals to the tracks. The tracks are parallel. A transversal is a line that intersects any two or more other lines. Transversals to parallel lines have interesting properties.

  7. 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? 1, 3, 5, and 7 all measure 150°. 2, 4, 6, and 8 all measure 30°.

  8. If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

  9. Additional Example 1 Continued Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1 2 1 @3 @ 5 @7 3 4 2 @4 @6 @8 5 6 7 8

  10. Try This 1: Example 1 Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1 2 4 3 5 6 8 7 1, 4, 5, and 8 all measure 36°. 2, 3, 6, and 7 all measure 144°.

  11. Try This 1: Example 1 Continued Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1 @4 @ 5 @8 2 @3 @6 @7 2 1 3 4 6 5 7 8

  12. Writing Math The symbol for parallel is ||. The symbol for perpendicular is .

  13. Lesson Quiz In the figure a || b. 1. Name the angles congruent to 3. 1, 5, 7 2. Name all the angles supplementary to 6. 1, 3, 5, 7 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60°

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