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Welcome! 1. Take out your homework and a red pen 2. Take out a protractor 3. Start working on the back of your notes from yesterday Row #? 3.2: Angles Formed by Parallel Lines and Transversals Learning Objective : SWBAT prove and use theorems about the angles formed by parallel lines and a transversal. Whiteboards: Review Identify each of the following. 1. a pair of parallel segments EH || FG 2. a pair of skew segments BF and EH 3. a pair of perpendicular segments CG GH 4. a pair of parallel planes plane ABC and plane EFG Whiteboards Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 3.2 Angles Formed by Parallel Lines and Transversals What would you call two lines that are on the same plane bdo not intersect? Exterior B A Interior D C Exterior • A solid arrow placed on two lines of a diagram indicate the lines are parallel. • The symbol || is used to indicate parallel lines. • AB || CD 3.2 Angles Formed by Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD B A D C 3.2 Angles Formed by Parallel Lines and Transversals Special Angle Relationships WHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles Exterior are CONGRUENT 1 3 4 Interior 5 6 7 8 Exterior 2 ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY 3.2 Angles Formed by Parallel Lines and Transversals Example 1 Find mQRS. 3.2 Angles Formed by Parallel Lines and Transversals Example 2 Find each angle measure. a. mECF b. mDCE 3.2 Angles Formed by Parallel Lines and Transversals Example 3 Find the measure of each angle. a. mEDG b. mBDG Example 4 Find mABD. 2x + 10° = 3x – 15° x = 25 mABD = 2(25) + 10 = 60° Alt. Int. s Thm. Subtract 2x and add 15 to both sides. Substitute 25 for x. Example 5: 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 5x + 5(5) = 60 x = 7, y = 5 Subtract the first equation from the second equation. Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x. Whiteboards State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m1 = 120°, m2 = (60x)° Alt. Ext. s Thm.; m2 = 120° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° Alt. Int. s Thm.; m3 = 120°, m4 =120° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Same-Side Int. s Thm.; m3 = 120°, m5 =60° Lesson Overview Standards: A.CED.3 MP: 1,2,3,4,5 Vocabulary: Transversal, …. Essential Question: Learning Objective: Prove and use theorems about the angles formed by parallel lines and a transversal. Independent Practice: Pg. 148 #6-13, 26-29, 34, 42