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3.2- Angles formed by parallel lines and transversals
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3-2 Properties of Parallel Lines
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EXAMPLE 1 Identify congruent angles
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Presentation transcript:

Concept

15  11 Corresponding Angles Postulate 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

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

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

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

Concept

Concept

Alternate Interior Angles Postulate 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 m2 = m3 125 = m3 Answer: m3 = 125 Alternate Interior Angles Postulate Definition of congruent angles Substitution Example 2

FLOOR TILES The diagram represents the floor tiles in Michelle’s house 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 A B C D Example 2

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

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

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

Concept

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