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Transcript
Section 3.3 Prove Lines are Parallel
Goal • Use angle relationships to prove that lines are parallel.
In Geometry, we have several theorems that help us determine if lines are parallel.
They are the true converses of the theorems we learned in the last section.
Example 1: Determine which of the following pairs of angles, fit into the given categories.
a. Corresponding angles
b. Alternate interior
c. Alternate exterior
d. Consecutive interior
POSTULATE 16 CORRESPONDING ANGLES CONVERSE
If two lines are cut by a transversal so the corresponding
angles are congruent, then the lines are parallel.
Example 2: Is enough information given to conclude that BD║EG? Justify your conclusion.
a.
b.
●
110º D
●
B
●
E
110º
●
G
Example 3: Find the value of x that
makes m║n.
B
E
64º
65º
D
G
Checkpoint: Find the value of x that
makes a║b.
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.
Section 3.3 Prove Lines are Parallel
THEOREM 3.5 ALTERNATE EXTERIOR ANGLES CONVERSE
If two lines are cut by a transversal so the alternate
exterior angles are congruent, then the lines are parallel.
THEOREM 3.6 CONSECUTIVE INTERIOR ANGLES CONVERSE
If two lines are cut by a transversal so the consecutive
interior angles are supplementary, then the lines are parallel.
Example 4: Find the value of x so that p║q.
a.
b.
Checkpoint: Use the diagram at the right.
a. Find the value of x that makes a || b.
b. Find the value of y that makes a || c.
Another way to determine if two lines are parallel is by the Transitive Property of Parallel
Lines:
THEOREM 3.7 TRANSITIVE PROPERTY OF PARALLEL LINES
If p║q and q║r, then p║r.
If two lines are parallel to the same line,
then they are parallel to each other.