Methods of Proving Lines are Parallel

CAP If two lines are cut by a transversal and the corresponding angles are congruent,

then the lines are parallel.

AIP If two lines are cut by a transversal and the alternate interior angles are congruent then the lines are parallel.

AEP If two lines are cut by a transversal and the alternate exterior angles are congruent then the lines are parallel.

SSISP If two lines are cut by a transversal and the same-side interior angles are supplements, then the lines are parallel.

SSESP If two lines are cut by a transversal and the same-side exterior angles are supplementary then the lines are parallel.

2P3P If two lines in a plane are perpendicular to a third line, then the lines are parallel.

TPL Transitive of Parallel Lines- If two lines are parallel to the same line, then the lines are parallel.

Converses

PCA If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

PAI If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

PAE If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

PSSIS If two parallel lines are cut by a transversal then the same-side exterior angles are supplementary.

PSSES If two parallel lines are cut by a transversal then the same-side exterior angles are supplementary.

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Methods of Proving a Quadrilateral is a Parallelogram

Def. If both pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

BSC If both pair of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

BAC If both pair of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

DB If the diagonals of a quadrilateral bisect each other, then it is a parallelogram

OPCP If one pair of sides is both congruent and parallel, then it is a parallelogram.

Methods of Proving a Parallelogram is a Rectangle

If a parallelogram has one right angle then it is a rectangle

If a parallelogram has congruent diagonals then it is a rectangle

Methods of Proving a Parallelogram is a Rhombus

If a parallelogram has two consecutive sides congruent, then it is a rhombus.

If a parallelogram has perpendicular diagonals then it is a rhombus.

If a parallelogram’s diagonal bisects a corner angle then it is a rhombus.

Methods of Proving a Parallelogram is a Square

To prove a parallelogram is a square you would need to prove it was both a rectangle and a rhombus.