3.3 – Proves Lines are Parallel
What is the definition of a converse?
Is the converse of a true conditional
statement always true?
3.3 – Proves Lines are Parallel
Postulate 16 – Corresponding Angles
Converse
If two lines are cut by a transversal so the
corresponding angles are congruent, then the
lines are parallel.
3.3 – Proves Lines are Parallel
Example 1: Apply the Corresponding
Angles Converse
Find the value of y that makes a // b.
3.3 – Proves Lines are Parallel
What is the difference between what you can
prove with the Corresponding Angles
Converse and the Corresponding Angles
Postulate?
3.3 – Proves Lines are Parallel
Theorem 3.4 – Alternate Interior Angles
Converse
If two lines are cut by a transversal so the
alternate interior angles are congruent, then
the lines are parallel.
3.3 – Proves Lines are Parallel
Theorem 3.4 – Alternate Exterior Angles
Converse
If two lines are cut by a transversal so the
alternate exterior angles are congruent, then
the lines are parallel.
3.3 – Proves Lines are Parallel
Theorem 3.4 – Consecutive Interior
Angles Converse
If two lines are cut by a transversal so the
consecutive interior angles are
supplementary, then the lines are parallel.
3.3 – Proves Lines are Parallel
Example 2:
Can you prove that lines a and b are parallel?
Explain why or why not?
3.3 – Proves Lines are Parallel
Example 3: Prove that if two lines are cut by
a transversal so the alternate interior angles
are congruent, then the lines are parallel.
3.3 – Proves Lines are Parallel
Example 4: In the figure, a // b and <1 is
congruent to <3. Prove c // d. Use a two
column or paragraph proof.
3.3 – Proves Lines are Parallel
Theorem 3.7 – Transitive Property of
Parallel Lines
If two lines are parallel to the same line, then
they are parallel to each other.
3.3 – Proves Lines are Parallel
Example 5: Use the Transitive Property of
Parallel Lines
In the figure each rung of the ladder is parallel
to the rung directly above it. Explain why the
top rung is parallel to the bottom rung.