Geometry 201 unit 3.2
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This document discusses properties of parallel lines and angles formed when lines are cut by a transversal. It defines key angle terms such as corresponding angles, alternate interior angles, and alternate exterior angles. Examples show how to use postulates and theorems about parallel lines to calculate unknown angle measures. Theorems addressed include the corresponding angles postulate and theorems about alternate interior and exterior angles. The document provides examples finding specific angle measures and asks students to identify the theorem or postulate used in different problems.
Geometry 201 unit 3.2
- 1. UNIT 3.2 PROPERTIESUNIT 3.2 PROPERTIES OF PARALLEL LINESOF PARALLEL LINES
- 2. 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. Prove and use theorems about the angles formed by parallel lines and a transversal. Objective
- 5. 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. 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. If a transversal is perpendicular to two parallel lines, all eight angles are congruent. Helpful Hint
- 8. 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. 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. 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. 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. 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. 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°
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