Gch3 l2
- 1. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals3-2 Angles Formed by Parallel Lines and Transversals Holt Geometry Warm UpWarm Up Lesson PresentationLesson Presentation Lesson QuizLesson Quiz
- 2. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Warm Up Identify each angle pair. 1. ∠1 and ∠3 2. ∠3 and ∠6 3. ∠4 and ∠5 4. ∠6 and ∠7 same-side int ∠s corr. ∠s alt. int. ∠s alt. ext. ∠s
- 3. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Prove and use theorems about the angles formed by parallel lines and a transversal. Objective
- 4. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals
- 5. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Find each angle measure. Example 1: Using the Corresponding Angles Postulate A. m∠ECF x = 70 B. m∠DCE m∠ECF = 70° Corr. ∠s Post. 5x = 4x + 22 Corr. ∠s Post. x = 22 Subtract 4x from both sides. m∠DCE = 5x = 5(22) Substitute 22 for x. = 110°
- 6. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 1 Find m∠QRS. m∠QRS = 180° – x x = 118 m∠QRS + x = 180° Corr. ∠s Post. = 180° – 118° = 62° Subtract x from both sides. Substitute 118° for x. Def. of Linear Pair
- 7. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals If a transversal is perpendicular to two parallel lines, all eight angles are congruent. Helpful Hint
- 8. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Remember that postulates are statements that are accepted without proof. Since the Corresponding Angles Postulate is given as a postulate, it can be used to prove the next three theorems.
- 9. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Find each angle measure. Example 2: Finding Angle Measures A. m∠EDG B. m∠BDG m∠EDG = 75° Alt. Ext. ∠s Thm. m∠BDG = 105° x – 30° = 75° Alt. Ext. ∠s Thm. x = 105 Add 30 to both sides.
- 10. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 2 Find m∠ABD. m∠ABD = 2(25) + 10 = 60° 2x + 10° = 3x – 15° Alt. Int. ∠s Thm. Subtract 2x and add 15 to both sides. x = 25 Substitute 25 for x.
- 11. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Find x and y in the diagram. Example 3: Music Application By the Alternate Interior Angles Theorem, (5x + 4y)° = 55°. By the Corresponding Angles Postulate, (5x + 5y)° = 60°. 5x + 5y = 60 –(5x + 4y = 55) y = 5 5x + 5(5) = 60 Subtract the first equation from the second equation. x = 7, y = 5 Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x.
- 12. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 3 Find the measures of the acute angles in the diagram. An acute angle will be 180° – 125°, or 55°. By the Alternate Exterior Angles Theorem, (25x + 5y)° = 125°. By the Corresponding Angles Postulate, (25x + 4y)° = 120°. The other acute angle will be 180° – 120°, or 60°.
- 13. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Lesson Quiz State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m∠1 = 120°, m∠2 = (60x)° 2. m∠2 = (75x – 30)°, m∠3 = (30x + 60)° Corr. ∠s Post.; m∠2 = 120°, m∠3 = 120° Alt. Ext. ∠s Thm.; m∠2 = 120° 3. m∠3 = (50x + 20)°, m∠4= (100x – 80)° 4. m∠3 = (45x + 30)°, m∠5 = (25x + 10)° Alt. Int. ∠s Thm.; m∠3 = 120°, m∠4 =120° Same-Side Int. ∠s Thm.; m∠3 = 120°, m∠5 =60°