Unformatted text preview: Available Euclidean Converses Theorem 3.4.1 (The "Alternate Interior Angles" Theorem): If two lines l and m are intersected by a transversal t such that
the alternate interior angles formed are congruent,
then the two lines e and m are parallel. Neutral Corollaries of the AIA Theorem Corollary 3.4.3 (The "Congruent Corresponding Angles" Theorem): If two lines 8 and m are intersected by a transversal t such that
a pair of congruent corresponding angles are formed,
then the two lines l and m are parallel. Corollary 3.4.4 (The"Supplementary Same—Side Interior Angles" Theorem): If two lines Z and m are intersected by a transversal t such that
the interior angles on the same side of t are supplementary,
then the two lines 2 and m are parallel. You can apply either of the corollaries by saying "By a corollary of the alternate interior angles theorem, . . . " The Converse of the Alternate Interior Angles Theorem: If two lines Z and m are parallel and are intersected by a transversal t ,
then the alternate interior angles formed are congruent. Euclidean Corollaries of the Converse of the AIA Theorem The Converse of the Congurent Corresponding Angles Theorem: If two lines 5 and m are parallel and are intersected by a transversal t ,
then the corresponding angles formed are congruent.. The Converse of the Supplementary SameSide Interior AnglesTheorem: If two lines 6 and m are parallel and are intersected by a transversal t ,
then the the interior angles on the same side of t are supplementary. You can apply either of the corollaries by saying
"By a corollary of the converse of the alternate interior angles theorem, . . . " ...
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 Spring '10
 Shirley

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