3.2 Use Parallel Lines and Transversals
(Textbook pg. 154)
Objective:
CA Standard(s):
Postulate
Linear pair Postulate
If two angles form a linear pair, then they are supplementary.
____________ for a linear pair, so
____________ are supplementary and
_____________________________
Theorem
Vertical Angles Congruence Theorem
Vertical angles are _____________.
Vocabulary
Key Vocabulary
Parallel Lines
Transversal
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Consecutive Interior Angles
Example 1
Postulate
Identify all pairs of angles of the given type.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
______________.
Example 2
Identify Congruent Angles
The measure of three of the numbered angles is
125°. Identify all angles. EXPLAIN your reasoning.
Checkpoint
Complete the following exercise using the diagram shown.
Theorem
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
_____________.
Theorem
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are
_____________.
Theorem
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are
_____________________.
Example 3
Use properties of parallel lines
Example 4
Use properties of parallel lines
Find the value of x.
Example 5
Use properties of parallel lines
Find the value of x.
Example 6
Use properties of parallel lines
Find the value of x.
Checkpoint
Complete the following exercise.
Learning Log:
1. What did you
learn?
2. Anything you
don’t
understand?
And why?
3. What helped
you
understand
this section?
Be sure to
include MATH
vocabulary.