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Warm ups Choose the plane parallel to plane MNR. Choose the segment skew to MP. Classify the relationship between <1 and <5. Classify the relationship between <3 and <8. Classify the relationship between <4 and <6. 3-2 ANGLES AND PARALLEL LINES Objective: Use theorems to determine relationships between specific pairs of angles. Use algebra to find angle measurements. Concept Example 1 A. In the figure, m<11 = 51. Find m<15. Tell which postulates (or theorems) you used. <15 is congruent to <11 Corresponding Angles Postulate m<15 = m<11 Definition of congruent angles m<15 = 51 Substitution Answer: m<15 = 51 Use Corresponding Angles Postulate Example 1 B. In the figure, m<11 = 51. Find m<16. Tell which postulates (or theorems) you used. <15 @ @ <16 @ m<16 = <16 m<16 <15 Vertical Angles Theorem <11 Corresponding Angles Postulate <11 Transitive Property m<11 Definition of congruent angles = 51 Answer: m<16 = 51 Use Corresponding Angles Postulate Substitution Example 1a A. In the figure, a || b and m<18 = 42. Find m<22. A. 42 B. 84 C. 48 D. 138 Example 1b B. In the figure, a || b and m<18 = 42. Find m<25. A. 42 B. 84 C. 48 D. 138 Parallel Lines and Angle Pairs Alternate Interior Angles Theorem Example 2 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m<2 = 125, find m<3. @ <2 Theorem m<2 = m<3 125 = m<3 <3 Alternate Interior Angles Definition of congruent angles Substitution Answer: m<3 = 125 Use Theorems about Parallel Lines Example 2 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m<2 = 125, find m<4. A. 25 B. 55 C. 70 D. 125 Example 3 A. ALGEBRA If m<5 = 2x – 10, and m<7 = x + 15, find x. @ <5 Postulate m<5 = m<7 2x – 10 = x + 15 x – 10 = 15 x = 25 Answer: x = 25 Find Values of Variables <7 Corresponding Angles Definition of congruent angles Substitution Subtract x from each side. Add 10 to each side. Example 3 B. ALGEBRA If m<4 = 4(y – 25), and m<8 = 4y, find y. <8 @ <6 Corresponding Angles Postulate m<8 = m<6 Definition of congruent angles 4y = m<6 Find Values of Variables Substitution Example 3 continued m<6 + m<4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution 4y + 4y – 100 = 180 Distributive Property 8y = 280 Add 100 to each side. y = 35 Divide each side by 8. Answer: y = 35 Find Values of Variables Try with a Mathlete A. ALGEBRA If m<1 = 9x + 6, m<2 = 2(5x – 3), and m<3 = 5y + 14, find x. A. x = 9 B. x = 12 C. x = 10 D. x = 14 TOO B. ALGEBRA If m<1 = 9x + 6, m<2 = 2(5x – 3), and m<3 = 5y + 14, find y. A. y = 14 B. y = 20 C. y = 16 D. y = 24 Concept Homework • Pg. 183 # 11 – 19, 25, 27, 29, 36, 43, 46