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**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 segmentsis not parallel to PT?**A.OS B.TS C.NR D.MQ 5-Minute Check 6**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**Use Corresponding Angles Postulate**A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used. 15 11 Corresponding Angles Postulate m15 =m11 Definition of congruent angles m15 =51 Substitution Answer: m15 = 51 Example 1**Use Corresponding Angles Postulate**B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used. 16 15 Vertical Angles Theorem 15 11 Corresponding Angles Postulate 16 11 Transitive Property () m16 = m11 Definition of congruent angles m16 = 51 Substitution Answer: m16 = 51 Example 1**A. In the figure, a || b and m18 = 42. Find m22.**A. 42 B. 84 C. 48 D. 138 Example 1a**B. In the figure, a || b and m18 = 42. Find m25.**A. 42 B. 84 C. 48 D. 138 Example 1b**Use Theorems about Parallel Lines**FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3. 2 3 Alternate Interior Angles Theorem m2 =m3 Definition of congruent angles 125 =m3 Substitution Answer:m3 = 125 Example 2**FLOOR TILES The diagram represents the floor tiles in**Michelle’s house. If m2 = 125, find m4. A. 25 B. 55 C. 70 D. 125 Example 2**Find Values of Variables**A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5 7 Corresponding Angles Postulate m5 =m7 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**Find Values of Variables**B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y. 8 6 Corresponding Angles Postulate m8 = m6 Definition of congruent angles 4y = m6 Substitution Example 3**Find Values of Variables**m6 + m4 = 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 m1 = 9x + 6, m2 = 2(5x – 3), and**m3 = 5y + 14, find x. A.x = 9 B.x = 12 C.x = 10 D.x = 14 Example 3**B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and**m3 = 5y + 14, find y. A.y = 14 B.y = 20 C.y = 16 D.y = 24 Example 3