Download Honors Geometry Section 3.4 Proving Lines Parallel

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Honors Geometry Section 3.4
Proving Lines Parallel
With the postulates and theorems
of Section 3.3, we are given that
lines are parallel and make
conclusions about the special angle
pairs. In this section, the process is
reversed as we look at the
converses of the postulates and
theorems from Section 3.3.
Postulate 3.4.1 CAP Converse
If two lines are cut by a transversal
and corresponding angles are
congruent, then the lines are
parallel.
Theorem 3.4.2 SSIAT Converse
If two lines are cut by a transversal
and same-side interior angles are
supplementary, then the lines are
parallel.
Theorem 3.4.3 AIAT Converse
If two lines are cut by a transversal
and alternate interior angles are
congruent, then the lines are
parallel.
Theorem 3.4.4 AEAT Converse
If two lines are cut by a transversal
and alternate exterior angles are
congruent, then the lines are
parallel.
Examples: Determine which lines, if any, will be parallel
based on the given information. If lines are parallel,
give a reason why (i.e. one of the converses).
a // c, AEATC
a // c, CAPC
d // e, SSIATC
Examples: Determine which lines, if any, will be parallel
based on the given information. If lines are parallel,
give a reason why (i.e. one of the converses).
None
None
a//b, AIATC
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