Section Three
Postulates
Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Ex. m ll n
Parallel Postulate: Through a point P not on a line l , there is exactly one line parallel to l.
Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Ex. m ll n
Parallel Postulate: Through a point P not on a line l , there is exactly one line parallel to l.
Theorems: Proving Lines Parallel
Converse of the Alternate Interior Angles Theorem: If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.
Converse of the Alternate Interior Angles Theorem: If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.
Converse of the Alternate Exterior Angles Theorem:If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel
Converse of the Same-Side Interior Angles Theorem: If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.
Converse of the Same-Side Interior Angles Theorem: If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.