Lesson 3 2 Angles Parallel Lines TARGETS Use

Lesson 3 -2: Angles & Parallel Lines TARGETS • Use theorems to determine the relationships between specific pairs of angles. • Use algebra to find angle measurements.

Content Standards G-CO. 1 Experiment with transformations in the plane. G-CO. 9 Prove geometric theorems. G-CO. 12 Make geometric constructions. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision.

LESSON 3 -2: Angles & Parallel Lines What is a Postulate? Describes a fundamental relationship between the basic terms of geometry Accepted to be true without proof

LESSON 3 -2: Angles & Parallel Lines What is a Theorem? A statement or conjecture that can be proven true by undefined terms, definitions and postulates.

LESSON 3 -2: Angles & Parallel Lines q Corresponding Angles Postulate If line q line r, then <1 or any other pair of corresponding angles r <6 5 1 8 4 2 3 6 7 d

LESSON 3 -2: Angles & Parallel Lines q Alternate Interior Angles Theorem If line q line r, then <1 r <3 1 or any other pair of alternate interior angles 4 2 3 d

LESSON 3 -2: Angles & Parallel Lines q Consecutive Interior Angles Theorem r If line q line r, then <1 and <2 are supplementary 1 or any other pair of consecutive interior angles 4 2 3 d

LESSON 3 -2: Angles & Parallel Lines q Alternate Exterior Angles Theorem If line q line r, then <5 or any other pair of alternate exterior angles <7 r 5 8 6 7 d

LESSON 3 -2: Angles & Parallel Lines q EXAMPLE 1 Use Theorems about Parallel Lines r A. In the figure, m 2 = 51. Find m 5. 5 (Tell which postulates (or theorems) you used. ) 1 8 4 2 3 6 7 d

LESSON 3 -2: Angles & Parallel Lines q EXAMPLE 1 Use Theorems about Parallel Lines r B. In the figure, m 5 = 51. Find m 7. (Tell which postulates (or theorems) you used. ) 5 1 8 4 2 3 6 7 d

LESSON 3 -2: Angles & Parallel Lines EXAMPLE 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m 2 = 125, find m 3. 2 3 m 2 = m 3 125 = m 3 Alternate Interior Angles Postulate Definition of congruent angles Substitution Answer: m 3 = 125

LESSON 3 -2: Angles & Parallel Lines EXAMPLE 3 Find Values of Variables A. ALGEBRA If m 4 = 2 x – 10, and m 5 = x + 15, find x. 4 5 m 4 = m 5 2 x – 10 = x + 15 x – 10 = 15 x = 25 Answer: x = 25 Alternate Exterior Definition of congruent angles Substitution Subtract x from each side. Add 10 to each side.

LESSON 3 -2: Angles & Parallel Lines EXAMPLE 3 Find Values of Variables B. ALGEBRA If m 4 = 4(y – 25), and m 8 = 4 y, find y. 8 6 Corresponding Angles Postulate m 8 = m 6 Definition of congruent angles 4 y = m 6 Substitution m 6 + m 4 = 180 4 y + 4(y – 25)= 180 4 y + 4 y – 100 = 180 Supplement Theorem Substitution Distributive Property 8 y = 280 Add 100 to each side. y = 35 Divide each side by 8. Answer: y = 35

LESSON 3 -2: Angles & Parallel Lines

LESSON 3 -2: Angles & Parallel Lines Perpendicular Transversal Theorem If line a line b and line a line t, then line b line t.