Types of Quadrilaterals

Quadrilaterals

A quadrilateral is a polygon with four sides and four vertices. It is also known as a four-sided polygon. The four sides of a quadrilateral may be straight or curved, but the sum of the internal angles of a simple quadrilateral must always be equal to 360 degrees. There are several different types of quadrilaterals based on their sides and angles.

Types of Quadrilaterals

1. Square: A square is a rectangle where all four sides are equal and each angle measures 90 degrees. All squares have fourth congruent right triangles as internal angles formed by the intersection of its diagonals. Additionally, they have two sets of perpendicular diagonals, dividing them into 4 congruent right triangles.

2. Rectangle: A rectangle is a quadrilateral whose opposite sides are parallel and congruent. It has only one pair of congruent angles (each measuring 90°), and these angles are called its "corners". Of all rectangles, those with acute angles are called rectangular parallelograms.

3. Trapezium: A trapezium is any quadrilateral with one pair of parallel sides. In other words, it has one base and one lateral side between the bases. Its diagonals bisect each other and have equal lengths.

4. Parallelogram: A parallelogram is a quadrilateral with both pairs of opposite sides parallel to each other. This means that the opposite sides are also congruent. One property of a parallelogram is that if you draw a diagonal through any vertex, then the other diagonal will also pass through that vertex.

Diagonals of a Quadrilateral

The diagonal of a quadrilateral is a line segment which joins two non-adjacent vertices. A parallelogram has no diagonal as its opposite sides are parallel. For a rectangle with opposite sides being parallel, there is only one way to draw diagonals, dividing it into four right triangles. In the case of a trapezium, if you extend the corresponding bases, they become the same length and make an angle with each other. The intersection of these extended bases forms angles equal to half of the given angles of the triangle formed by a pair of its adjacent sides.