In today's lesson, we will prove that the interacting diagonals of a parallelogram divide it into four triangles, all of which have equal areas. Each of the diagonals of a parallelogram divides it … [Read more...] about The Diagonals Divide a Parallelogram Into Four Equal Areas

# Parallelograms

A quadrangle in which both pairs of opposite sides are parallel to each other is called a parallelogram.

The opposite sides of a parallelogram are equal in size to each other, and the opposite angles are equal - as we will show, using triangle congruence.

Other properties include:

- The diagonals of a parallelogram bisect each other
- Any two adjacent angles are supplementary

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*Now that we've explained the basic concept of parallelograms in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Parallel Lines Drawn Through a Point on the Diagonal of a Parallelogram

One of the proofs done by Euclid in his "Elements" book, where he laid the foundation for geometry, is that if you draw lines parallel to the sides of a parallelogram and through any point on the … [Read more...] about Parallel Lines Drawn Through a Point on the Diagonal of a Parallelogram

## Parallelograms: Consecutive Angles are Supplementary

One of the basic properties of parallelograms is that any pair of consecutive angles are supplementary. This property will be very useful in many problems involving parallelograms. We'll prove this … [Read more...] about Parallelograms: Consecutive Angles are Supplementary

## Parallelograms: The Two Pairs of Opposite Angles are Congruent

A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. One of the properties of parallelograms is that the opposite angles are congruent, as we will now show. … [Read more...] about Parallelograms: The Two Pairs of Opposite Angles are Congruent

## Opposite Sides of a Parallelogram are Equal

In today's lesson, we will show that the opposite sides of a parallelogram are equal to each other. A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. We will … [Read more...] about Opposite Sides of a Parallelogram are Equal

## Proving that a Quadrilateral is a Parallelogram

A parallelogram is defined as a quadrilateral with two opposite pairs of sides are parallel. We have said (and proven) that parallelograms have four basic properties: The two pairs of opposite … [Read more...] about Proving that a Quadrilateral is a Parallelogram

## The Diagonals of a Parallelogram Bisect Each Other

In this lesson, we will prove that in a parallelogram, each diagonal bisects the other diagonal. A line that intersects another line segment and separates it into two equal parts is called a … [Read more...] about The Diagonals of a Parallelogram Bisect Each Other