Construction& Problem Solving

You will be able to use the converse of a theorem to construct parallel lines.

You will be able to use theorems to find the measures of angles formed by parallel lines and transversals.

Objectives

Vertical Angle Theorem – ◦ if angles are vertical angles, then their measures are

equal.

Axiom 1 – ◦ Things that are equal to the same thing are equal to each

other.

Supplementary Angles – ◦ add up to 180º.

Adjacent Angles – ◦ Adjacent angles are “side by side” and share a common

ray.

Starting with a review

3.3.1 Theorem – ◦ If two lines are parallel, then the interior angles

on the same side of the transversal are supplementary.

3.3.2 Theorem: ◦ If two lines cut by a transversal are parallel,

then the corresponding angles are equal. 3.3.3 Theorem:

◦ If two lines cut by a transversal are parallel then the alternate interior angles are equal.

Parallel Lines Theorems

If a transversal intersects two lines so that the alternate interior angles are equal, then the lines are parallel.

Converse of the theorem about parallel lines and alternate interior angles.

Alternate Interior Angles Postulate

The measure of 3 is three times that of 5.◦ m3 = 135o; m5 = 45o

Three times the m4 is two times that of 6◦ m4 = 72o; m 6 = 108o

m4 is 1/3 m3. What is the measure of m8?◦ m3 = 135o; m4 = 45o;

m8 = 45o

Practice