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Lesson 3-2

Lesson 3-2. Angles and Parallel Lines. Transparency 3-2. 5-Minute Check on Lesson 3-1. Refer to the figure. 1. Name all planes parallel to MNR . 2. Name all segments skew to MP . Give the special name for each angle pair in the figure. 3. 1 and 5 4. 3 and 8 5. 4 and 6

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Lesson 3-2

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  1. Lesson 3-2 Angles and Parallel Lines

  2. Transparency 3-2 5-Minute Check on Lesson 3-1 Refer to the figure. 1. Name all planes parallel to MNR. 2. Name all segments skew to MP. Give the special name for each angle pair in the figure. 3. 1 and 5 4. 3 and 8 5. 4 and 6 6. How many pairs of alternate interior angles are there in the figure above? Standardized Test Practice: A B C D 4 1 3 2

  3. Transparency 3-2 5-Minute Check on Lesson 3-1 Refer to the figure. 1. Name all planes parallel to MNR. Plane POS (can be named with any 3 letters from POST) 2. Name all segments skew to MP. TS, QR, NR, OS Give the special name for each angle pair in the figure. 3. 1 and 5 corresponding angles 4. 3 and 8 consecutive interior angles 5. 4 and 6 alternate exterior angles 6. How many pairs of alternate interior angles are there in the figure above? Standardized Test Practice: A B C D 4 1 3 2

  4. Objectives • Use the properties of parallel lines to determine congruent angles • Use algebra to find angle measures

  5. Vocabulary • No new vocabulary words or symbols

  6. t Parallel Lines and Transversals 1 2 k 4 3 5 6 l 7 8

  7. t k 1 2 3 4 5 6 l 7 8 Solving Angle Problems • 95% of all angle problems are solved by one of two equations: • Angle = Angle (angles are congruent) • Angle + Angle = 180 (angles are supplementary) Angle = Angle m1 = m8 3x + 10 = 4x – 30 +30 = +30 3x + 40 = 4x -3x = -3x 40 = x Angle + Angle = 180 m4 + m6 = 180 4x – 30 + x + 10 = 180 5x – 20 = 180 +20 = +20 5x = 200 x = 40

  8. In the figure x || y andm11 = 51. Find m16. Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution Answer:

  9. In the figure, a || b and m18 = 42. Find m19 and m 25 Answer: m19 = 138, and m25 = 42

  10. What is the measure of RTV? You need to find RTV. Be sure to identify it correctly on the figure. Look for patterns!!

  11. Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Addition Postulate

  12. Answer: 93 What is the measure ofIGE?

  13. ALGEBRA and If find x and y. by the Corresponding Angles Postulate. Find x. Definition of congruent angles Substitution Subtract x from each side and add 10 to each side.

  14. by the Alternate Exterior Angles Theorem. Find y. Definition of congruent angles Substitution Substitution Simplify. Add 100 to each side. Divide each side by 4. Answer:

  15. ALGEBRA: If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x and y. Answer: x = 12 and y = 20

  16. Decision Tree for Special  Pairs Consecutive Int Are they on opposite sides of transversal no yes Alt Interior both interior Corresponding Where are the two angles? Are they on opposite sides of transversal no one of each yes None both exterior None no Are they on opposite sides of transversal yes Alt Exterior

  17. Identification: Determine what each of these angle pairs are in the drawing below: Acute Angle: Alternate Interior Angles: Alternate Exterior Angles: Corresponding Angles: Consecutive Interior Angles: Linear Pair of Angles: Obtuse Angle: Right Angle: Vertical Angle Pair: 9 5 11 13 8 14 6 12 10 4 16 15 7 Answer: many combinations are possible

  18. ALGEBRA: If m4 = 2x + 16 and m4 = 2(4x – 3), find m1, and m4. 4 Answer: m1 = 130° m4 = 50°.

  19. ALGEBRA: If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find m1, m2, m3, and m4. 4 Answer: m1 = 114°, m2 = 114°, m3 = 114°, and m4 = 66°.

  20. Summary & Homework • Summary: • Pairs of congruent angles formed by parallel lines and a transversal are corresponding angles, alternate interior angles and alternate exterior angles • Pairs of consecutive interior angles are supplementary • Homework: • Day 1: pg 136 – 137: 1, 5-11, 14-19 • Day 2: pg 136 – 137: 20-25, 26, 27, 29, 31, 39

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