A **polygon** is a closed plane figure composed of at least three line segments that do not cross.

Properties of quadrilaterals include the number of parallel sides, angle measures, number of congruent sides, lines of symmetry, and the relationship between the diagonals.

Check the boxes to change the type of quadrilateral.

Drag the blue vertices to change the size and orientation of the shape.

Explore each shape. Move the vertices to adjust its size and orientation and write down what you notice about the:

- Sides
- Angles
- Diagonals
- Lines of symmetry

Place each shape in its appropriate place in the Venn diagram.

trapezoid | rectangle | square | parallelogram | rhombus |

Worked Solution

Place the shapes in order from smallest to greatest number of lines of symmetry.

Worked Solution

Idea summary

The properties of sides and angles of the different properties of quadrilaterals can be summarized as follows:

The properties of diagonals can be summarized as follows:

We've just learned all about some different properties of quadrilaterals. Let's explore whether there is any overlap.

Review the properties of all of the different types of quadrilaterals. Are there any shapes that satisfy all of the criteria of a different shape?

Are there any quadrilaterals that do not satisfy the the criteria for a different type of shape?

All of the shapes we've discussed are quadrilaterals because they have 4 sides. Quadrilaterals all share some properties, but they can be divided in to different subgroups based on additional properties that a given shape has.

Let's take a look at the quadrilateral hierachy:

Each shape belongs to all of the groups connected above it.

The Venn diagram is another way to visualize which groups a figure belongs to.

Some figures belong to multiple groups. When a shape belongs to multiple groups, the most precise classification is the group that is the most restrictive one (the one with the most properties).

For example, we see that a square is a rectangle, a rhombus, a parallelogram, and a quadrilateral. The most precise classification is the most detailed one, in this case a square.

It is also important to note that all squares are rectangles, but not all rectangles are squares.

A rhombus is a parallelogram and a quadrilateral, but the most precise classification is a rhombus.

A rectangle is also a parallelogram and a quadrilateral, but the most precise classification is a rectangle.

Consider what you know about parallelograms.

Which of the following quadrilaterals are not parallelograms?

A

B

C

D

E

Worked Solution

Patricia draws a quadrilateral, and covers it up. She tells Glen that the quadrilateral consists of right angles only. From this information, Glen knows that the quadrilateral is definitely a:

A

rhombus

B

square

C

trapezoid

D

rectangle

Worked Solution

For each of the shapes below, choose the most precise classification.

a

A

Trapezoid

B

Rectangle

C

Square

Worked Solution

b

A

Square

B

Trapezoid

C

Rectangle

Worked Solution

c

A

Trapezoid

B

Rectangle

C

Square

Worked Solution

d

A

Rhombus

B

Square

C

Rectangle

Worked Solution

A quadrilateral has exactly two lines of symmetry. Using only this information, which shape could it be? Select all that apply.

A

Rectangle

B

Square

C

Rhombus

D

Isosceles trapezoid

Worked Solution

Idea summary

Quadrilateral Hierarchy: