Splash Screen

Five-Minute Check (over Lesson 3–1) CCSS 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

G.CO.9 Prove theorems about lines and angles. Mathematical Practices Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.9 Prove theorems about lines and angles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

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

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

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

Concept

Concept

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

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 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

Concept

End of the Lesson