Type of Quadrilaterals…continued

__Rectangle__

__Definition:____ __A parallelogram where all the four angles are right angles is called a rectangle.

Properties:

1) Opposite sides are equal and parallel to each other.

2) Each angle measures

3) The diagonals are equal i.e.

4) The diagonals bisect each other

Theorem: The diagonals of a rectangle are equal.

Given: is a rectangle and the diagonals are

To prove:

Consider

(given that it is a rectangle)

is common

(right angles)

Hence (S.A.S axiom)

Therefore . Hence Proved

__Square__

A parallelogram which has all sides equal and all four angles are right angle is called a square. Or we can also say that a square is a rectangle that has all four sides equal.

Properties of square:

1) All sides are equal i.e.

2) Each angle measures

3) The diagonals are equal i.e.

4) The diagonals bisect each other

The diagonals intersect at right angles i.e.

Theorem: The diagonals of a square are equal and perpendicular to each other.

To prove:

Given: Square , Diagonals

Proof:

Consider

(given that it is a square)

is common

(right angles)

Hence (S.A.S axiom)

Therefore . Hence Proved

Consider

(diagonals of a parallelogram bisect each other)

is common

(Sides of a triangle)

Hence (S.S.S axiom)

Hence

We know that

Therefore

Hence