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Understanding Angles Formed by Parallel Lines and Transversals

This lesson presentation focuses on the angles formed when parallel lines are intersected by a transversal. Students will identify various angle pairs including corresponding angles, alternate interior and exterior angles, and same-side interior angles. Through engaging examples and quizzes, learners will prove and apply the theorems related to these angle relationships. Key concepts such as the Corresponding Angles Postulate and Alternate Interior Angles Theorem will be emphasized, enhancing students' understanding and problem-solving skills in geometry.

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Understanding Angles Formed by Parallel Lines and Transversals

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  1. Angles Formed by Parallel Lines and Transversals 3-2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  2. Warm Up Identify each angle pair. 1.1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 corr. s alt. int. s alt. ext. s same-side int s

  3. Objective Prove and use theorems about the angles formed by parallel lines and a transversal.

  4. Example 1: Using the Corresponding Angles Postulate Find each angle measure. A. mECF x = 70 Corr. s Post. mECF = 70° B. mDCE 5x = 4x + 22 Corr. s Post. x = 22 Subtract 4x from both sides. mDCE = 5x = 5(22) Substitute 22 for x. = 110°

  5. Check It Out! Example 1 Find mQRS. x = 118 Corr. s Post. mQRS + x = 180° Def. of Linear Pair Subtract x from both sides. mQRS = 180° – x = 180° – 118° Substitute 118° for x. = 62°

  6. Helpful Hint If a transversal is perpendicular to two parallel lines, all eight angles are congruent.

  7. 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.

  8. Example 2: Finding Angle Measures Find each angle measure. A. mEDG mEDG = 75° Alt. Ext. s Thm. B. mBDG x – 30° = 75° Alt. Ext. s Thm. x = 105 Add 30 to both sides. mBDG = 105°

  9. Check It Out! Example 2 Find mABD. 2x + 10° = 3x – 15° Alt. Int. s Thm. Subtract 2x and add 15 to both sides. x = 25 mABD = 2(25) + 10 = 60° Substitute 25 for x.

  10. Example 3: Music Application Find x and y in the diagram. 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 Subtract the first equation from the second equation. Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x. 5x + 5(5) = 60 x = 7, y = 5

  11. Check It Out! Example 3 Find the measures of the acute angles in the diagram. By the Alternate Exterior Angles Theorem, (25x + 5y)° = 125°. By the Corresponding Angles Postulate, (25x + 4y)° = 120°. An acute angle will be 180° – 125°, or 55°. The other acute angle will be 180° – 120°, or 60°.

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