QUADRILATERALS

A quadrilateral is a polygon with four sides. It has:

• Four sides (edges)
• Four vertices (corners)
• The interior angles add up to 360 degrees
• Two diagonals: a diagonal of a quadrilateral is a line segment whose end-points are opposite vertices of the quadrilateral. In picture below, ABCD is a quadrilateral, AC, BD are the two diagonals.

We name a quadrilateral by naming the four vertices in consecutive order. So we can name the quadrilateral as ABCD.

TYPES OF QUADRILATERALS

1. Parallelograms (paralelogramos)

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Also opposite angles are equal.

Types of parallelograms

 Square
 All sides equal, all angles 90°, the diagonals are equal and perpendicular.

 Rectangle
Opposite sides equal, all angles 90°, the diagonals are congruent but they are not perpendicular. 

Rhombus
Opposite sides parallel and equal, the diagonals are not equal but they are perpendicular.

Rhomboid
A rhomboid has opposite sides that are parallel and equal.

2. Trapezium (Trapecios- trapezoid US)

A trapezium is a quadrilateral with a pair of parallel sides.

The pair of parallel sides (SR||PQ) are called the bases of the trapezium, and the non-parallel sides (PS,QR) form the legs of the trapezium. The distance between the bases or the trapezium is called the height or the altitude. 

Types of trapeziums

If we have two right angles and two parallel sides, then we have an

rectangle trapezium

 

If the two legs of the trapezium are congruent to each other, then we have an isoceles trapezium

If the four sides or the trapezium have different lengths, then we have a scalene trapezium

 

3. Trapezoid (trapezoide)

A trapezoid (trapezium in US) is a quadrilateral with NO parallel sides

You can find a overview abour quadrilaterals here: