3-3 Proving Lines Parallel

3-3 Proving Lines Parallel

Today we learned 2 new postulates and four new theorems.

The new theorems were all converses of the theorems in lesson

3-2 (the ones we learned the day before).

The two new postulates were;

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

And the converse.

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

The first theorem was:If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

The next theorem was:
If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

In the example above, since ∠4 and ∠5 are supplementary, and ∠6 and ∠7 are also supplementary, then lines p and r are parallel.

The next theorem involves perpendicular lines:
In a plane two lines perpendicular to the same line are parallel.

The final theorem was:

Two lines parallel to a third line are parallel to each other.

Overall we learned the different ways to prove two lines are parallel

1. 1. Show that a pair of corresponding angles are congruent.
2. 2. Show that a pair of alternate interior angles are congruent.
3. 3. Show that a pair of same-side angles are supplementary.
4. 4. In a plane show that both lines are perpendicular to a third line.
5. 5. Show that both lines are parallel to a third line.

Andddd,the next scribe is….

Kristaa:33