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

3. Example 1 Use Corresponding Angles Postulate B. In the figure, m  11 = 51. Find m  16. Tell which postulates (or theorems) you used. Answer: m  16 = 51  15  11Corresponding Angles Postulate  15  16Substitution  11  16Supplement Theorem m  11=m  16Definition of Congruent Angles m  16=51Substitution

4. A.A B.B C.C D.D Example 1a A.42 B.84 C.48 D.138 A. In the figure, a || b and m  18 = 42. Find m  22.

5. A.A B.B C.C D.D Example 1b A.42 B.84 C.48 D.138 B. In the figure, a || b and m  18 = 42. Find m  25.

6. Concept Theorem--A statement that can be justified by logical reasoning and must be proven before it is accepted as true. Given: Segment BD is a median of triangle ABC. Segment DE is a median of triangle ADB. Segment DE is perpendicular to segment AB. Prove:Triangle DBC is isosceles.

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14. Example 2 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 Postulate m  2 = m  3 Definition of congruent angles 125 = m  3 Substitution Answer: m  3 = 125

15. A.A B.B C.C D.D Example 2 A.25 B.55 C.70 D.125 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  4.

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

17. B. ALGEBRA If m  4 = 4(y – 25), and m  8 = 4y, find y. Example 3 Find Values of Variables  8  6Corresponding Angles Postulate m  8=m  6Definition of congruent angles 4y=m  6Substitution

18. Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer: y = 35

19. A. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find x. A.A B.B C.C D.D Example 3 A.x = 9 B.x = 12 C.x = 10 D.x = 14

20. B. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find y. A.A B.B C.C D.D Example 3 A.y = 14 B.y = 20 C.y = 16 D.y = 24

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