Question

Types of Quadrilaterals with diegram​

Answer 1

Answer:

triangle, rhombus,parellogram, square, trapezium etc

Answer 2

There are six basic types of quadrilaterals:

1. Rectangle

Opposite sides are parallel and equal.

All angles are 90º.

The diagonals bisect each other.

A rectangle.

2. Square

Opposite sides are parallel and all sides are equal.

All angles are 90º.

Diagonals bisect each other at right angles.

A square.

3. Parallelogram

Opposite sides are parallel and equal.

Opposite angles are equal.

Diagonals bisect each other.

A parallelogram.

4. Rhombus

All sides are equal and opposite sides are parallel.

Opposite angles are equal.

The diagonals bisect each other at right angles.

A rhombus.

5. Trapezium

A trapezium has one pair of opposite sides parallel.

A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following diagram.

A trapezium.

6. Kite

Two pairs of adjacent sides are equal.

One pair of opposite angles is equal.

Diagonals intersect at right angles.

The longest diagonal bisects the shortest diagonal into two equal parts.

A kite.

Theorem 3

Prove that the angle sum of a quadrilateral is equal to 360º.

Proof:

A diagonal AC divides the quadrilateral ABCD into two triangles. q and v are two angles in triangle ACD and p and u are two angles in ABC.

In triangle ABC, p + u + B = 180 degrees {Angle sum of triangle} ...(1). In triangle ACD, q + v + D = 180 degrees {Angle sum of triangle} ...(2). Adding (1) and (2) gives (p + q) + (u + v) + B + D = 360 degrees so we find A + B + C + D = 360 degrees.

Hence the angle sum of a quadrilateral is 360º.