A quadrilateral is a polygon (i.e. 2D shape) with four edges (or sides) and four vertices or corners. Examples of quadrilaterals are illustrated below.
In this section we’ll focus on parallelograms and trapezoids. The videos below will prove the following three things:
- The diagonals of a parallelogram bisect each other.
- Joining the midpoints of adjacent sides of any quadrilateral forms a parallelogram.
- The line segment joining the midpoints of the non-parallel sides of a trapezoid is parallel to the parallel sides and has a length equal to the mean of the lengths of the parallel sides.
The next video will show how the length of the line segment joining the midpoints of the non-parallel sides is equal to the average lengths of the parallel sides.
The final video will show you how to prove that the diagonals of a parallelogram, namely a rhombus, bisect each other at 90°. Remember that a diagonal is a line segment connecting non-adjacent vertices. Let’s take a look: