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Understanding Parallel and Perpendicular Lines in Geometry

Enhance your knowledge of parallel and perpendicular lines, transversals, and angle properties in this comprehensive course. Learn to identify, measure, and work with different types of angles. Get ready to master geometric concepts!

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Understanding Parallel and Perpendicular Lines in Geometry

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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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