Converse Of Same Side Interior Angles Theorem Proof

Converse of same side interior angles postulate.

Converse of same side interior angles theorem proof. If two parallel lines are crossed by a transversal then each pair of same side interior angles is supplementary. Quadrilateral r e c t is shown with right angles at each of the four corners. Two column proof corresponding angles.

We know that a b and c are collinear and b is between a and c by construction because a and c are two points on the parallel line l on opposite sides of. That is if two lines k and l are cut by a transversal so that the alternate interior angles are congruent then k l. 4 1 5 3 the definition of congruent angles.

Converse of corresponding angles theorem. 2 m 1 m 3 vertical or opposite angles. Proof consecutive interior angles converse you same side interior angles proof you same side exterior angles definition theorem lesson converse of same side interior angles theorem algebra and whats people lookup in this blog.

Converse of same side interior angles theorem if two coplanar lines are crossed by a transversal so that a pair of same side interior angles is supplementary then the two lines are parallel. Then α θ and β γ by the alternate interior angle theorem. Alternate interior angles theorem converse of the alternate interior angles theorem converse of the same side interior angles theorem same side.

Prove converse of alternate interior angles theorem. Assume l m and the above angle assignments. Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.

Assume l m and prove same side interior angles are supplementary. 3 m 1 m 5 using 1 and 2 and transitive property of equality both equal m 3. The converse of this theorem is also true.