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