Presentation on theme: "Then/Now You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles."— Presentation transcript:
1Then/NowYou named angle pairs formed by parallel lines and transversals.Use theorems to determine the relationships between specific pairs of angles.Use algebra to find angle measurements.
3Use Corresponding Angles Postulate Example 1A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.What is the relationship between < 11 and < 15?15 11 Corresponding Angles Postulatem15 = m11 Definition of congruent anglesm15 = 51 Substitutionm< 15 = 51
4Use Corresponding Angles Postulate Example 1B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.16 15 Vertical Angles Theorem15 11 Corresponding Angles Postulate16 11 Transitive Property ()m16 = m11 Definition of congruent anglesm16 = 51 Substitution
5Example 1b B. In the figure, a || b and m18 = 42. Find m25. A. 42 C. 48D. 138
10Example 3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Find Values of VariablesExample 3A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.5 7 Corresponding Angles Postulatem5 = m7 Definition of congruent angles2x – 10 = x Substitutionx – 10 = 15 Subtract x from each side.x = 25 Add 10 to each side.Answer: x = 25
11Example 3 B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y. Find Values of VariablesExample 3B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.8 6 Corresponding Angles Postulatem8 = m6 Definition of congruent angles4y = m6 Substitution
12Example 3 m6 + m4 = 180 Supplement Theorem Find Values of VariablesExample 3m6 + m4 = 180 Supplement Theorem4y + 4(y – 25) = 180 Substitution4y + 4y – 100 = 180 Distributive Property8y = 280 Add 100 to each side.y = 35 Divide each side by 8.Answer: y = 35