Objectives:-Define transversal, alternate interior, alternate exterior, same side interior, and corresponding angles-Make conjectures and prove theorems by using postulates and properties of parallel lines and transversals

3.3 Parallel Lines & Transversals

Warm-Up: What weighs more: a pound of feathers or a pound of bricks?

Transversal:

a line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.

Interior & Exterior Angles:

Interior

Exterior

Exterior

Alternate Interior Angles:

1 2

3 4

5 67 8

If two lines cut by a transversal are parallel then, alternate interior angles are congruent.

Alternate Interior Theorem:

Proof: The Alternate Interior Angles Theorem

Given:

Prove:

Statements Reasons

Alternate Exterior Angles:

1 2

3 4

5 6

7 8

Alternate Exterior Angle Theorem:

If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.

Proof: The Alternate Exterior Angles Theorem

Given:

Prove:Statements Reasons

Same Side Interior Angles:

1 2

3 4

5 6

7 8

If two lines cut by a transversal are parallel, then same side interior angles are supplementary.

Same Side Interior Angle Theorem:

Proof: The Same Side Interior Angles Theorem

Given:

Prove:

Statements Reasons

Corresponding Angles: 1 2

3 4

5 6

7 8

Corresponding Angles Postulate:

If two lines cut by a transversal are parallel, then corresponding angles are congruent.

Example:1 2

3 4

5 6

7 8

List all of the angles that are congruent to <1:

List all of the angles that are congruent to <2:

Identify each of the following:

alternate interior angles:

alternate exterior angles:

same side interior angles:

corresponding angles:

Example: 1 2

3 4

5 6

7 8If m<1 = find the measurements of each of the remaining angles in the figure.

m<4 =

m<5 =

m<8 =

m<2 =

m<3 =

m<6 =

m<7=

Example: 1 2

3 4

5 6

7 8

If m<3 = and m<7 = find the measurements of each of the angles in the figure.

m<1 =

m<4 =

m<5 =

m<8 =

m<2 =

m<3 =

m<6 =

m<7 =

Example: 1 2

3 4

5 6

7 8

If m<3 = and m<5 = find the measurements of each of the angles in the figure.

m<1 =

m<4 =

m<5 =

m<8 =

m<2 =

m<3 =

m<6 =

m<7 =

Example:In triangle KLM, NO is parallel to ML and <KNO is congruent to <KON. Find the indicated measures.

m<KNO =

m<NOL =

m<MNL =

m<KON =

m<LNO =

m<KLN =

K

N O

M L

𝟗𝟐𝟎

𝟒𝟒𝟎 𝟐𝟐𝟎

HOMEWORK: page 159-160 #’s 5-12, 22-33