Angles and Parallel Lines LESSON 3–2 Angles and Parallel Lines

Five-Minute Check (over Lesson 3–1) TEKS Then/Now Postulate 3.1: Corresponding Angles Postulate Example 1: Use Corresponding Angles Postulate Theorems: Parallel Lines and Angle Pairs Proof: Alternate Interior Angles Theorem Example 2: Real-World Example: Use Theorems about Parallel Lines Example 3: Find Values of Variables Theorem 3.4: Perpendicular Transversal Theorem Lesson Menu

Choose the plane parallel to plane MNR. A. RST B. PON C. STQ D. POS 5-Minute Check 1

Choose the segment skew to MP. A. PM B. TS C. PO D. MQ ___ 5-Minute Check 2

Classify the relationship between 1 and 5. A. corresponding angles B. vertical angles C. consecutive interior angles D. alternate exterior angles 5-Minute Check 3

Classify the relationship between 3 and 8. A. alternate interior angles B. alternate exterior angles C. corresponding angles D. consecutive interior angles 5-Minute Check 4

Classify the relationship between 4 and 6. A. alternate interior angles B. alternate exterior angles C. corresponding angles D. vertical angles 5-Minute Check 5

Which of the following segments is not parallel to PT? A. OS B. TS C. NR D. MQ 5-Minute Check 6

Mathematical Processes G.1(A), G.1(G) Targeted TEKS G.6(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems. Mathematical Processes G.1(A), G.1(G) TEKS

You 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. Then/Now

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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

16  15 Vertical Angles Theorem 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

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

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

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2  3 Alternate Interior Angles Theorem 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

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 Example 2

5  7 Corresponding Angles Postulate Find Values of Variables A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Explain your reasoning 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

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 Corresponding Angles Postulate m8 = m6 Definition of congruent angles 4y = m6 Substitution Example 3

m6 + m4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution Find Values of Variables 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 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 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 Example 3

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Angles and Parallel Lines LESSON 3–2 Angles and Parallel Lines