Proofs with Quadrilaterals

Proving Quadrilaterals are Parallelograms Show that opposite sides are parallel by same slope. Show that both pairs of opposite sides are congruent by distance formula. Show that diagonals bisect each other by midpoint formula. Showing 90 degree angle by perpendicular slopes.

Ways to prove a quadrilateral is a parallelogram If both pairs of opposite sides are parallel then it’s a parallelogram If both pairs of opposite sides are congruent

Ways to prove it’s a rectangle If the diagonals of a parallelogram are congruent then it’s a rectangle If one angle of a parallelogram is a right angle, then it’s a rectangle

Ways to prove it’s a Rhombus If the diagonals of a parallelogram are congruent then it’s a rhombus If two consecutive sides are congruent then it’s a rhombus

Ways to prove it’s a kite If the diagonals of a kite are perpendicular and there are no parallel lines, then it’s a kite.