3.2 – Use Parallel Lines and Transversals
Postulate 15 – Corresponding Angles
Postulate
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
3.2 – Use Parallel Lines and Transversals
Example 1: Identify congruent angles
The measure of three of the numbered angles is
55 degrees. Identify the angles. Explain your
reasoning.
What are the measures of the
other angles in the picture?
3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Alternate Interior Angles
Theorem
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
congruent.
3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Alternate Exterior Angles
Theorem
If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles
are congruent.
3.2 – Use Parallel Lines and Transversals
Theorem 3.1 – Consecutive Interior
Angles Theorem
If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles
are supplementary.
3.2 – Use Parallel Lines and Transversals
Example 2 – Use properties of parallel
lines
Find the value of x.
3.2 – Use Parallel Lines and Transversals
Example 3 – Use properties of parallel
lines
Find the value of x.
3.2 – Use Parallel Lines and Transversals
Example 4 – Use properties of parallel
lines
Find the value of x.
3.2 – Use Parallel Lines and Transversals
Example 5 – Use properties of parallel
lines
Find the value of x and y.
3.2 – Use Parallel Lines and Transversals
Example 6 – Use properties of parallel
lines
Find the value of x and y.
3.2 – Use Parallel Lines and Transversals
Example 7 – Use properties of parallel
lines
Find the value of x and y.
3.2 – Use Parallel Lines and Transversals
Example 8 – Prove the Alternate Interior
Angles Theorem
Prove that if two parallel lines are cut by
a transversal, then the pairs of alternate
interior angles are congruent.
3.2 – Use Parallel Lines and Transversals
Example 9 – Solve a real world problem.
When sunlight enters a drop of rain,
different colors of light leave the drop at
different angles. This process is what
makes a rainbow. For violet light, m<2 =
40 degrees. What is m<1? How do you
know?