Transcript Proving Lines Parallel

Proving Lines Parallel
Postulate 3.4 – Converse of Corresponding Angles
Postulate
• If two lines in a plane are cut by a transversal so
that corresponding angles are congruent, then the
lines are parallel.
Parallel Postulate
• If given a line and a point not on the line, then
there exists exactly one line through the point that
is parallel to the given line.
Proving Lines Parallel
Theorem 3.5 – Converse of Alternate Exterior
Angles Theorem
• If two lines in a plane are cut by a transversal so
that a pair of alternate exterior angles is congruent,
then the lines are parallel.
Theorem 3.6 – Converse of Consecutive Interior
Angles Theorem
• If two lines in a plane are cut by a transversal so
that a pair of interior angles on the same side of
the transversal is supplementary, then the lines are
parallel.
Proving Lines Parallel
Theorem 3.7 – Converse of Alternate Interior
Angles Theorem
• If two lines in a plane are cut by a transversal so
that a pair of alternate interior angles is congruent,
then the lines are parallel.
Theorem 3.8 – Converse of Perpendicular
Transversal Theorem
• In a plane, if two lines are perpendicular to the
same line, then they are parallel.
Determine which lines, if any, are parallel.
Answer:
ALGEBRA Find x and mGBA so that
Answer:
Answer: Since the slopes are not equal, r is not parallel to s.