3.2. ANGLES AND PARALLEL LINES Honors Geometry

Do Now True or False? If False, explain why.  <1 and <2 are supplementary  <1 and <7 are corresponding angles  <7 and <2 are alternate interior angles  <3 and <5 are consecutive interior angles  < 7 and <6 are congruent.

Homework Questions? Comments? Confusions?

Important Note: Important note: These relationships only work if you have PARALLEL lines cut by a transversal!

Postulate Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

Pause: Postulate vs. theorem. Difference!?!?!?

Example One: Find the measure of each angle if m<5 = 72.

Example Two: Find x. What’s the one thing missing from the picture?

You Try! If m<a is 5x + 12 and m<e is x + 80, find a, b, c, d, e, f, g, and h.

Alternate Interior Angles Theorem

How do we know?

Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. Ex: < 3 and < 2 are supplementary < 6 and < 7 are supplementary

Alternate Exterior Angles Theorem

Example Three:

Example Four: Find x

You Try! Find x and y and y

Example Five:

Example Six:

Example Seven:

You Try! Find the measure of angles 1, 2, 3 and 4.

Perpendicular Transversal Theorem a b t

Example Eight:

You Try! Find x

Practice Problems Try some on your own/in you table groups As always if you have any questions please don’t hesitate to ask me and/or your peers at your table! They are your greatest resource!

Exit Ticket: If m<3=4y+30 and m<7=7y+6, Find y