1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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 = 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

10. 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

11. 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

12. 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 Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
Example 3

13. 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

14. LESSON 3-2: Angles & Parallel Lines
Concept

15. 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