Identify trapeziums

Key notes:

Definition of Trapezium:

  • A trapezium (or trapezoid in American English) is a four-sided polygon (quadrilateral) with at least one pair of parallel sides. The parallel sides are called the bases, while the other two sides are called the legs.

Types of Trapeziums:

  • Isosceles Trapezium: Both legs are of equal length, and the angles adjacent to each base are equal.
  • Scalene Trapezium: The legs are of different lengths, and the angles adjacent to each base are also different.

Properties of Trapeziums:

  • Sum of Interior Angles: The sum of the interior angles of any quadrilateral, including trapeziums, is always 360 degrees.
  • Base Angles: In an isosceles trapezium, the angles on each base are equal. For example, if one angle is AAA at the top base, then the angle at the bottom base directly across from it is also AAA.
  • Height: The height of a trapezium is the perpendicular distance between the two bases.

Identifying a Trapezium:

  • To identify a trapezium, look for the following characteristics:
    • Four sides (quadrilateral).
    • At least one pair of parallel sides.
    • Check if the other pair of sides (legs) are equal in length (for isosceles trapeziums).

Learn with an example

➡️ Is this polygon a trapezium?

  • yes
  • no

To see if a polygon is a trapezium, first check that it is a quadrilateral. Then check that it has one pair of parallel sides.

This polygon has four sides. It is a quadrilateral.

However, this quadrilateral has no pairs of parallel sides. Parallel sides are usually marked with matching arrows.

So, it is not a trapezium.

➡️ Is this polygon a trapezium?

  • yes
  • no

To see if a polygon is a trapezium, first check that it is a quadrilateral. Then check that it has one pair of parallel sides.

This polygon has four sides. It is a quadrilateral.

However, this quadrilateral has no pairs of parallel sides. Parallel sides are usually marked with matching arrows.

So, it is not a trapezium.

➡️ Is this polygon a trapezium?

  • yes
  • no

To see if a polygon is a trapezium, first check that it is a quadrilateral. Then check that it has one pair of parallel sides.

This polygon has four sides. It is a quadrilateral.

This quadrilateral also has a pair of parallel sides. Parallel sides are usually marked with matching arrows.

So, it is a trapezium.

Let’s practice!🖊️