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Insert Lesson Title Here Properties of Parallel Lines Insert Lesson Title Here Vocabulary Transversal Supplementary Angles Vertical Angles Corresponding Angles Alternate Interior Angles Same Side Interior Angles

Parallel Lines 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.

Properties of Parallel Lines 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

PROPERTIES OF TRANSVERSALS TO PARALLEL LINES Properties of Parallel Lines 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.

Example 1: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l || line m. Find the measure of the angle. 4 All obtuse angles in the figure are congruent. m4 = 124°

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

Example 3: Finding Angle Measures of Parallel Lines Cut by Transversals Continued In the figure, line l || line m. Find the measure of the angle. 6 All acute angles in the figure are congruent. m6 = 56° Course 3

Parallel Lines m7 = 144° Example 4 In the figure, line n || line m. Find the measure of the angle. 7 All obtuse angles in the figure are congruent m7 = 144° 1 144° 3 4 5 6 7 8 m n

Example 5 In the figure, line n || line m. Find the measure of the angle. 5 5 is supplementary to the angle 144°. 1 144° 3 4 5 6 7 8 m n m5 + 144° = 180° –144° –144° m 5 = 36°

Example 6 In the figure, line n || line m. Find the measure of the angle. 1 All acute angles in the figure are congruent m1 = 36° 1 144° 3 4 5 6 7 8 m n

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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