Quadrilaterals

Concept

In geometry, a quadrilateral is a closed shape that is formed by joining four points among which any three points are non-collinear. A quadrilateral has 4 sides, 4 angles, and 4 vertices. ‘Quadrilateral’ is derived from a Latin word, in which, ‘Quadra’ means four and ‘Latus’ means sides. All 4 sides of a quadrilateral may or may not be equal.

Although a quadrilateral always has four sides, four angles, and four vertices, the measure of the sides and angles differ. It is to be noted that the sum of the interior angles of a quadrilateral is always equal to 360°. Below are the different types of quadrilaterals.

Rules

A square is a quadrilateral because it has 4 sides. It is also a parallelogram because opposite sides are parallel. It is a special rectangle with 4 right angles and 4 congruent sides.

A rhombus is a quadrilateral because it has 4 sides. It is also a parallelogram because opposite sides are congruent. However, it is not a rectangle because it does not have 4 right angles. Instead, it has 2 acute and 2 obtuse angles.

A trapezoid is a quadrilateral because it has 4 sides. However, it is not a parallelogram because two of its sides are not parallel. It is also not a rectangle, because it does not always have right angles. Instead, it has 2 acute and 2 obtuse angles and one pair of parallel sides.

Example

The family tree shows how the quadrilaterals are connected to each other.

Are all squares rhombuses?

Solution

Yes, all squares are rhombuses as a square is a quadrilateral with 4 equal-length sides and opposite sides parallel to each other just like a rhombus.

Practice Quadrilaterals

Practice Problem 1

Select all rectangles.
Remember: A rectangle has 4 right angles. Its opposite sides are equal and parallel.

Practice Problem 2

The family tree shows how the quadrilaterals are connected to each other.

Select whether the below statement is true or false.
Every trapezoid is a rectangle.