Ch 4.3 Transversals and Corresponding Angles Transversals & Corresponding Angles Ch 4.3 Transversals and Corresponding Angles Learning Target: I will be able to use theorems to determine the relationships between specific pairs of angles and to use algebra to find angle measurements Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal.

Ch 4.3 Transversals & Corresponding Angles Postulate 4-1 Concept

Ch 4.3 Transversals & Corresponding Angles Use Corresponding Angles Postulate A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used. 15  11 Corresponding Angles Postulate m15 = m11 Definition of congruent angles m15 = 51 Substitution Answer: m15 = 51 Example 1

Ch 4.3 Transversals & Corresponding Angles Use Corresponding Angles Postulate B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used. 16  15 Vertical Angles Theorem 15  11 Corresponding Angles Postulate 16  11 Transitive Property () m16 = m11 Definition of congruent angles m16 = 51 Substitution Answer: m16 = 51 Example 1

Ch 4.3 Classwork #1 A. In the figure, a || b and m18 = 42. Find m22. Transversals & Corresponding Angles Classwork #1 A. In the figure, a || b and m18 = 42. Find m22. A. 42 B. 84 C. 48 D. 138 Example 1a

Ch 4.3 Classwork #1 B. In the figure, a || b and m18 = 42. Find m25. Transversals & Corresponding Angles Classwork #1 B. In the figure, a || b and m18 = 42. Find m25. A. 42 B. 84 C. 48 D. 138 Example 1b

Ch 4.3 Transversals & Corresponding Angles 4-1 4-2 4-3 Concept

Ch 4.3 Transversals & Corresponding Angles Concept

Ch 4.3 Transversals & Corresponding Angles Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3. 2  3 Alternate Interior Angles Theorem m2 = m3 Definition of congruent angles 125 = m3 Substitution Answer: m3 = 125 Example 2

Ch 4.3 Transversals & Corresponding Angles Classwork #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 2

Ch 4.3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Transversals & Corresponding Angles Find Values of Variables A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5  7 Corresponding Angles Postulate m5 = m7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 = 15 Subtract x from each side. x = 25 Add 10 to each side. Answer: x = 25 Example 3

Ch 4.3 B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y. Transversals & Corresponding Angles Find Values of Variables 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 Substitution m6 + m4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution 4y + 4y – 100 = 180 Distributive Property 8y = 280 Additive Inverse Property. y = 35 Multiplicative Inverse Property. Example 3

Ch 4.3 Transversals & Corresponding Angles Classwork #3 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 Example 3

Ch 4.3 Transversals & Corresponding Angles Classwork #3 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 Example 3

Ch 4.3 Transversals & Corresponding Angles Theorem 4-4 Concept