Lesson 2:(3.2) Proving Lines Parallel

What are we learning?

Students will…To use a transversal and prove lines are parallel.

Evidence Outcome: Prove geometric theorems (lines, angles, triangles, parallelograms).

Purpose (Relevancy): To show how to paint parallel lines on a parking lot.

Proving Lines Parallel

1l

m 2

Postulate 3-2: Converse (Opposite) of Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

Limon Language: If corresponding angles are congruent, then the lines are parallel.

l ||m

Proving Lines Parallel

If Alternate Interior Angles are congruent we can assume lines are parallel too!

We know these two lines are

parallel!!

Proving Lines Parallel

Theorem 3-5: Converse of Alternate Interior Angles TheoremIf two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Limon Language: If alternate interior angles are congruent, then the lines are parallel.

If 12, then l ||m.

l

m

1 42

Proof of Theorem 3-5 (C of AIAT)

13

2

l

m

Given : 2 1

Prove : l ||m

Statements Reasons

1.

2.

3.

4.

1.

2.

3.

4.

Vertical 's are

2 3

2 1

l ||m

Proving Lines Parallel

If Same-Side Interior Angles are supplementary, we can assume lines are parallel too!!

We know these two lines are

parallel!!

Proving Lines Parallel

Theorem 3-6: Converse of Same-Side Interior Angles TheoremIf two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Limon Language: If same side interior angles add up to 180 degrees, then the lines are parallel.

.|| then ary,supplement are 4 and 2 If ml

l

m

1 42

Proving Lines Parallel

If Alternate Exterior Angles are congruent, we can assume lines are parallel!!!

We know these two lines are

parallel!!

Proving Lines Parallel

Theorem 3-7: Converse of Alternate Exterior Angles TheoremIf two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel.

Limon Language: If alternate exterior angles are congruent, then the lines are parallel.

.|| then ,21 If ba

a

b

1

3 2

Proof of Theorem 3-7 (C of AEAT)

1

2

a

b

Given : 2 1

Prove : a ||b

4

Statements Reasons

1.

2.

3.

4.

1.

2.

3.

4.

14

2 4

a ||b

Proving Lines Parallel

If Same-Side Exterior Angles are supplementary, we can assume lines are parallel!!!

We know these two lines are

parallel!!

Proving Lines Parallel

Theorem 3-8: Converse of Same-Side Exterior Angles TheoremIf two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel.

Limon Language: If same-side exterior angles add up to 180 degrees, then the lines are parallel.

If 1 and 3 are supplementary, then a ||b.

a

b

1

3 2

Let’s Apply What We Have Learned, K?

(2x + 6)°

40°

Find the value of x for which l || m

l

m

You Try One!

(7x - 8)°

62°

Find the value of x for which a || b

a

b

(3.2): Proving Lines Parallel(3.2): Proving Lines Parallel

My momma always said, “Life was like a box of chocolates. You never know what you’re gonna get.”

-Forrest

Homework: (3.2) Pg. 137-139; 1-8

all, 14-22 all, 24-30 even