Pre-Algebra 5.2 Parallel and Perpendicular Lines

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 Warm Up

Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

parallel lines perpendicular lines transversal Vocabulary

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

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°. Example: Identifying Congruent Angles Formed by a Transversal

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

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

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   Try This Continued

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.

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

In the figure, line l || line m. Find the measure of the angle. A. 4 m  4 = 124° All obtuse angles in the figure are congruent. Example: Finding Angle Measures of Parallel Lines Cut by Transversals

B. 2 m ° = 180° 2 is supplementary to the angle 124°. m2 = 56° –124° In the figure, line l || line m. Find the measure of the angle. Example: Finding Angle Measures of Parallel Lines Cut by Transversals Continued

All acute angles in the figure are congruent. C. 6 m  6 = 56° In the figure, line l || line m. Find the measure of the angle. Example: Finding Angle Measures of Parallel Lines Cut by Transversals Continued

In the figure, line n || line m. Find the measure of the angle. A. 7 m  7 = 144° All obtuse angles in the figure are congruent 1 144° m n Try This

B. 5 m ° = 180° 5 is supplementary to the angle 144°. m2 = 36° –144° 1 144° m n In the figure, line n || line m. Find the measure of the angle. Try This

All acute angles in the figure are congruent C. 6 m  6 = 36° 1 144° m n In the figure, line n || line m. Find the measure of the angle. Try This

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.

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