1. Objective: To indentify angles formed by two lines and a transversal.
Chapter 3 Lesson 1
Objective: To indentify angles formed by two lines and a transversal.

2. transversal: a line that intersects two coplanar lines at two distinct points.m
transversal
alternate interior angles: nonadjacent interior angles that lie on opposite sides of the transversal. t l 1 4 m 3 2

3. same-side interior angles: lie on the same side of the transversal and between l and m.1 4 m 3 2
corresponding angles: lie on the same side of the transversal and in corresponding positions relative to l and m. t l 6 5 1 4 m 3 2 8 7

4. Example 1: Identifying Angles
Name a pair of alternate interior angles and a pair of same-side interior angles. t l 6 5
3 and 4 are alternate interior angles
1 and 3 are same-side interior angles. 4 1 m 2 3 7 8

5. Example 2: Identifying Angles
Name all pairs of corresponding angles. t l 1 2 3 4 5 6 7 8 6 5
5 and 2; and ; 6 and 3; 1 and 8 4 1 m 2 3 7 8

6. Example 3: Identifying Angles
Identify which angle forms a pair of same-side interior angles with Identify which angle forms a pair of corresponding angles with
Same-Side 8 4 1 8 5 3 2 7 6
Corresponding 5

7. Postulate 3-1: Corresponding Angles Postulate If a transversal intersects two parallel lines, then corresponding angles are congruent. t 1 ► l 2 ► m
Theorem 3-1: Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. t ► l 1 2 ► m

8. Theorem 3-2: Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary. t ► l 1 2 ► m

9. Two-Column Proof of Theorem 3-1
two-column proof: steps that prove a theorem
Example 4 :
Two-Column Proof of Theorem 3-1 t
Given: 4 ► a 3 1
Prove: ► b
Statements
Reasons
1.)
2.)
3.)
4.)
Given
If lines are , then corr. are
Vertical angles are congruent
Transitive Property of Congruence

10. Two-Column Proof of Theorem 3-2
Example 5:
Two-Column Proof of Theorem 3-2 t
Given: 3 ► a 2
Prove: are supplementary. 1 ► b
Statements
Reasons
1.)
2.)
3.)
4.)
5.)
Given
Angle Add. Postulate
Corresponding Angles Postulate
Substitute
Def. of Supplementary Angles
are supplementary

11. Example 6: Finding Measures of Angles◄ ▲ a b c d 1 5 3 4 2 6 7 8
50°
Find ,and then Which theorem or postulate justifies each answer?
Since , because corresponding angles are congruent (Corresponding Angles Postulate).
Since , because same-side interior angles are supplementary (Same-Side Interior Angles Theorem).

12. Example 7: Finding Measures of Angles
Find the measure of each angle. Justify each answer. ◄ ▲ a b c d 1 5 3 4 2 6 7 8
50°
a.)
130; corr. angles are congruent
b.)
130; vert. angles are congruent
c.)
50; alt. int. angles are congruent
d.)
50; alt. int. angles are congruent
e.)
130; same-side int. angles are supp.
f.)
50; corr. angles are congruent or vert. angles are congruent

13. Example 8: Using Algebra to Find Angle Measures
Find the values of x and y.
x=70
70+50+y=180
120+y=180
y=60
Corresponding angles ▲ ▲
50°
Angle Add. Post. x° y°
70°
Simplify
Subtr. Prop of Equality

14. Example 9: Using Algebra to Find Angle Measures► a° c° b°
Find the values of a, b, and c. m
65°
40° ►
a = Alt. Int. Angles
c= Alt. Int. Angles
65+40+b = Angle Add. Post.
105+b=180 Simplify
b=75 Subtr. Prop. Of Equality

15. Assignment pg
#1-25