Lesson 3 2 Angles and Parallel Lines Transparency

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 1 5, 2 6, 3 7, 4 8 Corresponding Angles Post. then each pair of corresponding angles is congruent Alternate Interior Angles Thrm then each pair of alternate interior angles is 3 6, 4 5 congruent 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

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

In the figure, a || b and m 18 = 42. Find m 19 and m 25 Answer: m 19 = 138 , and m 25 = 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 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 Simplify. Add 100 to each side. Divide each side by 4. Answer:

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

Decision Tree for Special Pairs no ye s b int oth er ior Are they on opposite sides of transversal Where are the two angles? one of each Are they on opposite sides of transversal no ye s th bo rior te ex Are they on opposite sides of transversal no ye s Consecutive Int Alt Interior Corresponding 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 m 4 = 2 x + 16 and m 4 = 2(4 x – 3), find m 1, and m 4. 4 Answer: m 1 = 130° m 4 = 50°.

ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x – 3), and m 3 = 5 y + 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°.

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