Lesson 3-2 Angles and Parallel Lines
5-Minute Check on Lesson 3-1 Transparency 3-2 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: ACBD
5-Minute Check on Lesson 3-1 Transparency 3-2 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: ACBD
Objectives Use the properties of parallel lines to determine congruent angles Use algebra to find angle measures
Vocabulary No new vocabulary words or symbols
Parallel Lines and Transversals Postulate/ Theorem 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 m 3 + m 5 = 180°, m 4 + m 6 = 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 t k l
Answer: Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution In the figure x || y and m 11 = 51 . Find m 16.
Answer: m 19 = 138 , and m 25 = 42 In the figure, a || b and m 18 = 42 . Find m 19 and m 25
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 Definition of congruent angles Alternate Interior Angles Theorem Angle Addition Postulate Substitution
What is the measure of IGE? Answer: 93
If ALGEBRAand 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.
Definition of congruent angles Substitution Find y. by the Alternate Exterior Angles Theorem. Simplify. Add 100 to each side. Divide each side by 4. Answer: Substitution
Answer: x = 12 and y = 20 ALGEBRA: If m 1 = 9x + 6, m 2 = 2(5x – 3), and m 3 = 5y + 14, find x and y.
Decision Tree for Special Pairs Where are the two angles? Are they on opposite sides of transversal Are they on opposite sides of transversal Are they on opposite sides of transversal None Alt Exterior Consecutive Int Alt Interior both interior one of each both exterior yes Corresponding None yes no
Answer: many combinations are possible 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:
Answer: m 1 = 130° m 4 = 50°. ALGEBRA: If m 4 = 2x + 16 and m 4 = 2(4x – 3), find m 1, and m 4. 4
Answer: m 1 = 114°, m 2 = 114°, m 3 = 114°, and m 4 = 66°. 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
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, –Day 2: pg 136 – 137: 20-25, 26, 27, 29, 31, 39