What are the Properties of Quadrilaterals?

A shape hierarchy shows the flow of the shapes through their properties. The top level being the least complex type of shape to the more complex shapes.

This is a basic shape hierarchy for quadrilateral. It is missing aline between rhombus and square though. Because a rhombus can be a square. See if you can follow the hierarchy to expand your quadrilateral knowledge.

A quadrilateral has the following properties.

Four sided polygon with 4 sides and 4 vertexes or vertices.

This is a 2 dimensional shape that is a broad term that represents a series of more complex shapes.

• 4 Sides
• Closed Figure

What is a closed figure? A figure that starts and stops at the same point without lines crossing. try the finger trace test, you should be able to trace the figure with your finger and not go over any lines or parts ore than once.

Many types of shapes can be a quadrilateral, both regular and irregular. We are going to be talking about the regular shapes from this point further.

A parallelogram is always a quadrilateral. This quadrilateral has additional properties that also make it a parallelogram. The additional attribute that a parallelogram has is the parallel sides. Opposite sides of the parallelogram are parallel.

A parallelogram has two sets of parallel sides. The attribute of a parallelogram are:

• 4 sides
• closed figures
• 2 sets of parallel sides

A trapezoid is a quadrilateral but not a parallelogram. So it has the properties of a quadrilateral but not those of a parallelogram.

A trapezoid has the following attributes:

• 4 sides
• Closed figure
• One set of parallel lines

The difference between the parallelogram is that is only has a single set of parallel lines, this give the shape many different looks when looking at trapezoids.

A rectangle has all of the attributes of a parallelogram and a quadrilateral. It also has one additional attribute. It has right angles at the corners.

The rectangle has the following attributes:

• 4 sides
• closed figure
• 2 sets of parallel lines
• 4 right angles

Remember that a right angle is 90 degrees and looks like a corner.

A rhombus is a quadrilateral and a parallelogram. It is on a different branch than the rectangle and does not has the properties of a rectangle.

A rhombus has the following attributes:

• 4 sides
• Closed figure
• 2 sets of parallel sides
• 4 congruent sides - all sides have the same length

Note that the difference between this and a square is that there is no right angles in a rhombus.

A square is a quadrilateral, a parallelogram, a rectangle, and has one additional feature.

All of the side lengths are congruent or the same.

A square has the following attributes:

• 4 sides
• Closed figure
• 2 sets of parallel lines
• 4 right angles
• 4 sides with the same length

A square is a specific type of quadrilateral with many attributes.