Transcript Section 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 6. How many pairs of alternate interior angles are there in the figure above? Standardized Test Practice: A 1 B 2 C 3 D 4 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 1 B 2 C 3 D 4 Objectives • Use the properties of parallel lines to determine congruent angles • Use algebra to find angle measures Vocabulary • No new vocabulary words or symbols t Parallel Lines and Transversals Postulate/ Theorem k 3 l 5 7 1 2 4 6 8 Statement If two parallel lines are cut by a transversal, Examples Corresponding Angles Post. then each pair of corresponding angles is congruent 1 5, 2 6, 3 7, 4 8 Alternate Interior Angles Thrm then each pair of alternate interior angles is congruent 3 6, 4 5 Consecutive Interior Angles Thrm then each pair of consecutive interior angles is supplementary m3 + m5 = 180°, m4 + m6 = 180° Alternate Exterior Angles Thrm then each pair of alternate exterior angles is congruent 1 8, 2 7 Perpendicular Transversal Thrm In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. None illustrated In the figure x || y and m11 = 51. Find m16. Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution Answer: In the figure, a || b and m18 = 42. Find m19 and m 25 Answer: m19 = 138, and m25 = 42 What is the measure of RTV? You need to find RTV. Be sure to identify it correctly on the figure. Look for patterns!! 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 What is the measure of IGE? Answer: 93 ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate. Definition of congruent angles Substitution Subtract x from each side and add 10 to each side. Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Substitution Simplify. Add 100 to each side. Divide each side by 4. Answer: ALGEBRA: If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x and y. Answer: x = 12 and y = 20 Decision Tree for Special Pairs Are they on opposite sides of transversal Where are the two angles? one of each Are they on opposite sides of transversal Are they on opposite sides of transversal Consecutive Int Alt Interior Corresponding None None Alt Exterior Identification: Determine what each of these angle pairs are in the drawing below: Acute Angle: Alternate Interior Angles: 9 5 11 13 14 8 6 12 10 4 16 15 7 Alternate Exterior Angles: Corresponding Angles: Consecutive Interior Angles: Linear Pair of Angles: Obtuse Angle: Right Angle: Vertical Angle Pair: Answer: many combinations are possible ALGEBRA: If m4 = 2x + 16 and m4 = 2(4x – 3), find m1, and m4. 4 Answer: m1 = 130° m4 = 50°. ALGEBRA: If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find m1, m2, m3, and m4. 4 Answer: m1 = 114°, m2 = 114°, m3 = 114°, and m4 = 66°. 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