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

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. Targets

Accepted to be true without proof 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 Postulate

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. Theorem

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

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

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

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

Ex 1 : Use Theorems about Parallel Lines 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. (Tell which postulates (or theorems) you used.) 5 1 8 4 2 6 3 7 d Ex 1 : Use Theorems about Parallel Lines

Ex 1 : Use Theorems about Parallel Lines 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 6 3 7 d Ex 1 : Use Theorems about Parallel Lines

2  3 Alternate Interior Angles Postulate 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 Alternate Interior Angles Postulate m2 = m3 Definition of congruent angles 125 = m3 Substitution Answer: m3 = 125 Example 2

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

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

LESSON 3-2: Angles & Parallel Lines Concept

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