Use transformations, triangle congruency criteria, and line and angle relationship to prove parallelogram properties.

Let's prove to ourselves that if we have two diagonals of a quadrilateral that are bisecting each other, that we are dealing with a parallelogram. So let me see.

If a quadrilateral has all right angles and congruent sides, then it is a square. So both the original statement and its converse (switching the hypothesis and conclusion) are both true.

Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about …

Watch Sal classify a quadrilateral as a square, rhombus, rectangle, parallelogram, or trapezoid given its four vertices. Created by Sal Khan.

Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about …

A parallelogram, the diagonals bisect each other. For a rhombus, where all the sides are equal, we've shown that not only do they bisect each other but they're perpendicular bisectors of each other.

There are other ways of finding the areas of parallelograms, generally. It's essentially base times height, but for a rhombus we could do that because it is a parallelogram, but we also have this other neat …

Review the following quadrilaterals: parallelogram, trapezoid, rhombus, rectangle, and square. Then, try some practice problems.

I want to do a quick argument, or proof, as to why the diagonals of a rhombus are perpendicular. So remember, a rhombus is just a parallelogram where all four sides are equal.