Download Proving Lines Parallel

Proving Lines Parallel
Lesson 3.3
Pre-AP Geometry
Objectives
1. State and apply the postulates and theorems
about parallel lines.
2. State and apply the theorems about a parallel
and perpendicular to a given line through a
point outside the line.
Postulate 10
If two parallel lines are cut by a transversal, then
corresponding angles are congruent.
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Postulate 11
If two lines are cut by a transversal and
corresponding angles are congruent, then the
lines are parallel.
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Theorem 3-5
If two lines are cut by a transversal and alternate
interior angles are congruent, then the lines are
parallel.
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Theorem 3-6
If two lines are cut by a transversal and sameside interior angles are supplementary, then the
lines are parallel.
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Theorem 3-7
In a plane two lines perpendicular to the same
line are parallel.
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Theorem 3-8
Through a point outside a line, there is exactly
one line parallel to the given line.
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Theorem 3-9
Through a point outside a line, there is exactly
one line perpendicular to the given line.
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Theorem 3-10
Two lines parallel to a third line are parallel to
each other.
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Proving Lines Parallel
• Show that a pair of corresponding angles are
congruent.
• Show that a pair of alternate interior angles are
congruent.
• Show that a pair of same side interior angles are
supplementary.
• In a plane show that both lines are
perpendicular to a third line.
• Show that both lines are parallel to a third line.