{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

avail-eucl-converses

# avail-eucl-converses - Available Euclidean Converses...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 Same-Side 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, . . . " ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online