1. Transversals and Parallel Lines
Mod 14.2:
Transversals and Parallel Lines
Essential Question: How can you prove and use theorems about angles formed by transversals that intersect parallel lines?
CASS: G-CO.9 Prove theorems about lines and angles.
MP.3 Logic

2. Transversal
Transversal is a line that intersects two or more coplanar lines at two different points.

3. A transversal is a line that intersects two or more coplanar lines at different points.1 2 3 4 5 6 7 8 t t 2 1 4 3 5 6 7 8
corresponding angles
“same location”
1 & 5 are
1 & 8 are
alternate exterior angles

4. alternate interior angles 3 & 5 are1 2 3 4 5 6 7 8 t 1 2 3 4 5 6 7 8 t
3 & 6 are
alternate interior angles
3 & 5 are
Same side interior angles

5. Identifying Angle Relationships
EXAMPLE 1
Identifying Angle Relationships
List all angle pairs that fit the description. 4 3 2 1 8 7
a. corresponding 6 5
b. alternate interior
d. vertical
c. same side interior

6. SAME SIDE INTERIOR ANGLES POSTULATE
If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. 7 8
ALTERNATE INTERIOR ANGLES THEOREM
If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 3 4

7. ALTERNATE EXTERIOR ANGLES THEOREM
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. 1 8
CORRESPONDING ANGLES THEOREM
If two parallel lines are cut by a transversal, then corresponding angles are congruent. 1 2

8. Find Missing Angle Measures
EXAMPLE 2
Find Missing Angle Measures
Given that m∠ 1 = 75°, find each measure and explain your reasoning. 3 1 5 6 7 8 4 2
a. m∠ 3
105°; Linear Pair Postulate
b. m∠ 8
75°; Corresponding Angles Postulate
c. m∠ 5
75°; Vertical Angles are congruent
d. m∠ 4
75°; Vertical angles are congruent

9. Use properties of parallel lines to find the value of x.
TRY THIS
Use properties of parallel lines to find the value of x. 1
Vertical angles are congruent
Same side Interior Angles Postulate
Substitute

10. TRY THIS a b 1 2 5 6
If a||b and c||d and m∠ 2 = 99°; find each measure below and explain your reasoning 3 4 7 8 c 9 10 13 14 d 11 12 15 16
m∠ 4 =
81°
m∠ 7 =
99°
m∠ 11 =
99°
m∠ 5 =
81°
m∠ 16 =
81°

11. Using Properties of Parallel Lines
EXAMPLE 3
Using Properties of Parallel Lines
Use properties of parallel lines to find the value of x.

12. pp. 694 #1-14 all Key Content: ASSIGNMENTS Parallel Lines Transversal
Same-Side Interior Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles Postulate
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem