& 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.

 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.

 Theorem – ◦ If two lines are parallel, then the interior angles on the same side of the transversal are supplementary.  Theorem: ◦ If two lines cut by a transversal are parallel, then the corresponding angles are equal.  Theorem: ◦ If two lines cut by a transversal are parallel then the alternate interior angles are equal.

 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.

 The measure of  3 is three times that of  5. ◦ m  3 = 135 o ; m  5 = 45 o  Three times the m  4 is two times that of  6 ◦ m  4 = 72 o ; m  6 = 108 o  m  4 is 1/3 m  3. What is the measure of m  8? ◦ m  3 = 135 o ; m  4 = 45 o ; m  8 = 45 o