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Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ .

7-2. Parallel and Perpendicular Lines. Course 3. 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 ______________.

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Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ .

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  1. 7-2 Parallel and Perpendicular Lines Course 3 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

  2. 7-2 Parallel and Perpendicular Lines Course 3 Problem of the Day The square root of 1,813,141,561 is a whole number. Is it odd or even? How do you know? Odd: An odd number can only be the product of two odd numbers.

  3. 7-2 Parallel and Perpendicular Lines Course 3 Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

  4. 7-2 Parallel and Perpendicular Lines Course 3 Insert Lesson Title Here Vocabulary parallel lines perpendicular lines transversal

  5. 7-2 Parallel and Perpendicular Lines Course 3 Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. Perpendicular lines are lines that intersect at 90° angles.

  6. 7-2 Parallel and Perpendicular Lines Course 3 The railroad ties are transversals to the tracks. The tracks are parallel. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties.

  7. 7-2 Parallel and Perpendicular Lines Caution! You cannot tell for certain if angles are congruent by measuring because measurement is not exact. Course 3

  8. 7-2 Parallel and Perpendicular Lines Course 3 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°.

  9. 7-2 Parallel and Perpendicular Lines Course 3 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. 7-2 Parallel and Perpendicular Lines Course 3 Check It Out: 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. 7-2 Parallel and Perpendicular Lines Course 3 Check It Out: 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. 7-2 Parallel and Perpendicular Lines Course 3 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.

  13. 7-2 Parallel and Perpendicular Lines Course 3

  14. 7-2 Parallel and Perpendicular Lines Writing Math The symbol for parallel is ||. The symbol for perpendicular is . Course 3

  15. 7-2 Parallel and Perpendicular Lines Course 3 Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. All obtuse angles in the figure are congruent. 4 m4 = 124°

  16. 7-2 Parallel and Perpendicular Lines –124° –124° Course 3 Additional Example 2B: 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° m2 = 56°

  17. 7-2 Parallel and Perpendicular Lines Course 3 Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued In the figure, line l || line m. Find the measure of the angle. All acute angles in the figure are congruent. 6 m6 = 56°

  18. 7-2 Parallel and Perpendicular Lines 144° 1 m 4 3 6 5 n 8 7 Course 3 Check It Out: Example 2A In the figure, line n || line m. Find the measure of the angle. All obtuse angles in the figure are congruent 7 m7 = 144°

  19. 7-2 Parallel and Perpendicular Lines 144° 1 m 4 3 6 5 n 8 7 –144° –144° Course 3 Check It Out: Example 2B In the figure, line n || line m. Find the measure of the angle. 5 5 is supplementary to the angle 144°. m5 + 144° = 180° m5 = 36°

  20. 7-2 Parallel and Perpendicular Lines 144° 1 m 4 3 6 5 n 8 7 Course 3 Check It Out: Example 2C In the figure, line n || line m. Find the measure of the angle. All acute angles in the figure are congruent 1 m1 = 36°

  21. 7-2 Parallel and Perpendicular Lines Course 3 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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