Download Honors Geometry Lesson 3-2: Using Parallel Lines and Transversals

Honors Geometry Lesson 3-2: Use Parallel Lines and Transversals
Corresponding Angles Postulate: If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are congruent.
Example 1: The measure of three of the numbered angles is 125°. Identify the measure of the other angles.
EXPLAIN your reasoning.
Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are congruent.
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are congruent.
Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are supplementary.
Example 2: Find the value of x.
Example 3: Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles
are congruent.
Given: p║q
Prove: 1  2
Statements
Reasons
1.) ____________________________________
1.) _____________________________________
2.) ____________________________________
2.) _____________________________________
3.) ____________________________________
3.) _____________________________________
4.) ____________________________________
4.) _____________________________________
Example 4: Prove that if two parallel lines are cut by a transversal, then the exterior angles on the same side of
the transversal are congruent.
Given: p║q
Prove: 1 and 2 are supplementary
Statements
Reasons
1.) ____________________________________
1.) _____________________________________
2.) ____________________________________
2.) _____________________________________
3.) ____________________________________
3.) _____________________________________
4.) ____________________________________
4.) _____________________________________
5.) _____________________________________
5.) _____________________________________
6.) _____________________________________
6.) _____________________________________
Example 5: A taxiway is being constructed that intersects two parallel runways at an airport. You know that
m2 = 98°. What is m1? How do you know?