Each of the diagonals of a parallelogram divides it into two congruent triangles, as we saw when we proved properties like that the opposite sides are equal to each other or that the two pairs of … [Read more...] about The Diagonals Divide a Parallelogram Into 4 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 properties of parallelograms is that any pair of consecutive angles are supplementary. This is a straightforward application of the properties of parallel lines intersected by a transversal … [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. Since … [Read more...] about Parallelograms: The Two Pairs of Opposite Angles are Congruent

## Parallelograms: The Opposite Sides are Equal to Each Other

A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. We will show that in that case, they are also equal to each other.ProblemABCD is a parallelogram, … [Read more...] about Parallelograms: The Opposite Sides are Equal to Each Other

## Proving 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 a Quadrilateral is a Parallelogram

## The Diagonals of a Parallelogram Bisect Each Other

A line that intersects another line segment and separates it into two equal parts is called a bisector. In a quadrangle, the line connecting two opposite corners is called a diagonal. We will show … [Read more...] about The Diagonals of a Parallelogram Bisect Each Other