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

5-2 Parallel and Perpendicular Lines Warm Up Complete each sentence. Pre-Algebra 5-2 Parallel and Perpendicular Lines 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

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

Vocabulary parallel lines perpendicular lines transversal

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.

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.

PROPERTIES OF TRANSVERSALS TO PARALLEL LINES If two parallel lines are intersected by a transversal, the acute angles that are formed are all congruent, the obtuse angles are all congruent, and any acute angle is supplementary to any obtuse angle. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles.

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°.

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.

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 1 @  3 @  5 @  7 2 3 4 2 @  4 @  6 @  8 6 5 7 8

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

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 1 2 3 4 5 6 7 8

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

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°