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Transcript
3.2 Angles and Parallel Lines Objectives Use the properties of parallel lines to determine congruent angles Use algebra to find angle measures Postulate 3.1 Corresponding s Postulate If 2 lines are cut by a transversal, then each pair of corres. s is . 1 2 l m i.e. If l m, then 12. Theorem 3.1 Alternate Interior s Theorem If 2 lines are cut by a transversal, then each pair of alternate interior s is . l 1 2 m i.e. If l m, then 12. Theorem 3.2 Consecutive Interior s Theorem If 2 lines are cut by a transversal, then each pair of consecutive int. s is supplementary. l 1 m 2 i.e. If l m, then 1 & 2 are supplementary or m1 + m2 = 180°. Theorem 3.3 Alternate Exterior s Theorem If 2 lines are cut by a transversal, then the pairs of alternate exterior s are . l m 1 2 i.e. If l m, then 12. Theorem 3.7 Transversal Theorem If a transversal is to one of 2 lines, then it is to the other. t l m 1 2 i.e. If l m, & t l, then t m. Example 2: 1 125o Find: m1 = m2 = m3 = m4 = m5 = m6 = x= 55° 125° 55° 2 3 5 4 125° 55° 125° 40° x+15o 6 Example 3: What is the measure of RTV? Example 3: Alternate Interior Angles Theorem Definition of congruent angles Substitution Example 3: Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Addition Postulate Answer: RTV = 125° Example 4: ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate. Example 4: Definition of congruent angles Substitution Subtract x from each side and add 10 to each side. Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Example 4: Simplify. Add 100 to each side. Divide each side by 4. Answer: Your Turn: and ALGEBRA If find x and y. Answer: Assignment Geometry: Pg. 136 – 138 #14 – 27, 32 – 35, 39 Pre-AP Geometry: Pg. 136 – 138 #14 - 39