Types of quadrilaterals

A quadrilateral is any closed shape with four straight sides. The family is big , squares, rectangles, parallelograms, rhombuses, trapeziums. Each member has its own special properties.

What is this?

Let us meet the family:

• Square , all four sides equal, all four angles right angles.
• Rectangle , opposite sides equal, all four angles right angles.
• Parallelogram , opposite sides equal and parallel, but the angles are not all right angles.
• Rhombus , all four sides equal, but the angles are not all right angles. Looks like a tilted square , a diamond shape.
• Trapezium , only one pair of opposite sides parallel.

Every square is also a rectangle (since it has all right angles), and every rectangle is also a parallelogram (since opposite sides are parallel and equal). The family overlaps.

All quadrilaterals have one thing in common: their four angles always add up to 360°.

To draw a quadrilateral neatly:

1. Mark four dots , the corners.
2. Join them in order using a ruler.
3. The shape closes back at the first dot.

Make sure the four sides do not cross each other , otherwise you get a "bow-tie", which is not a simple quadrilateral.

Worked examples

Example 1. A shape has 4 sides, all equal, all corners right angles. What is it?

• Square.

Example 2. A quadrilateral has 4 sides, all equal, but no right angles. What is it?

• Rhombus.

Example 3. Three angles of a quadrilateral are 100°, 80°, 70°. Find the fourth.

• Sum = 360°.
• Fourth = 360 − 100 − 80 − 70 = 110°.

Try it

1. Sides 6, 6, 4, 4 cm with right angles. What is it?
2. Sides 5, 5, 5, 5 cm with no right angles. What is it?
3. Three angles are 90°, 90°, 90°. Find the fourth.
4. Is every square also a rectangle? Why?
5. Three angles of a quadrilateral are 70°, 110°, 90°. Find the fourth.

Hands-on

Match-stick shapes. Take 8 matchsticks and arrange them into different quadrilaterals , a square (4 sticks), a rectangle (longer + shorter), a rhombus (slanted square). Note how the lengths and angles change.

Tile detective. Find a tiled floor in your school or home. Identify the kind of quadrilaterals used. Draw a small section in your notebook.