G-U2b-Definitions&Parallel Lines

Created by:

mrs--nelson  on September 12, 2008

Description:

Properties of Parallel Lines

OAG-Geometry

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G-U2b-Definitions&Parallel Lines

 Parallel LinesTwo lines are parallel if and only if they are coplanar and do not intersect. (biconditional)
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Definitions

Parallel Lines Two lines are parallel if and only if they are coplanar and do not intersect. (biconditional)
skew lines lines that do not intersect but are coplanar
transversal a line that cuts across at least 2 other lines which may or may not be parallel
|| Symbol for parallel lines
corresponding angles angles in the same position with respect to the transveral and cut lines. If lines are parallel then the angles are congruent.
alternate exterior angles angles outside the cut lines and on opposite sides of transversal. If lines are parallel then the angles are congruent.
alternate interior angles angles on the inside of the cut lines and opposite sides of the transversal. If lines are parallel then the angles are congruent.
same side interior (also called consecutive interior) angles on the same side of transversal and inside the cut lines. If lines are parallel then the angles are SUPPLEMENTARY.
slopes of parallel lines the slopes are congruent
conditional statement If hypothesis, then conclusion (p->q)
converse If conclusion, then hypothesis (q->p)
inverse formed by negating (NOT) both the hypothesis and the conclusion (~p->~q)
contrapositive If NOT conclusion, then NOT hypothesis (~q->~p)
counterexample any situation that would make the logic statement false
biconditional when the conditional AND the converse are both true you combine using "if and only if" (iff)

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