Types of quadrilaterals

Group A Group B

A B

CD

∴ m∠ A, ∠B, ∠C & ∠D = 90°. Sides AB, BC, CD & DA are CONGRUENT

A quadrilateral with all congruent sides and each angle a right angle is called a square.

PROPERTIES OF SQUARE

O

P Q

RS

1] l (PR) = l (QS)

Diagonals of square are congruent.2] l(PO) = l(OR) & l(SO)= l(OQ)

The diagonals of a square bisect each other.

R S

TU

3] m∠ROS = m∠SOT = m∠UOT = m∠UOR = 90°.

It means that the diagonals of a square is perpendicular bisector of the other.

T h u s , e a c h d i a g o n a l s o f a s q u a r e i s p e r p e n d i c u l a r b i s e c t o r o f t h e o t h e r .

O

A B

CD

� ABCD is a quadrilateral.

m∠A , ∠B , ∠C , ∠D =90°.

∴� ABCD is a rectangle.

A quadrilateral with each angle a right angle is called a rectangle.

RECTANGLE

P Q

R S

1] In a � PQRS,Side PQ and side RS are congruentSimilarly side PR and side QS are also congruent.Thus, it means that,Opposite sides of a rectangle are congruent.

2] l(PS) = l(QS),The diagonals of the rectangle are congruent.

P Q

S R

O

TRAPEZIUM

A B

D C

PARALLELOGRAM

R S

TU

In � RSTU,side RS is parallel to side UT & side RU is parallel to side ST.

PROPERTISE OF PARALLELOGRAM

L M

NP

1] In � LMNP,seg. LM ≅ seg. PN,Similarly, seg LP ≅ seg MNTherefore,The opposite sides of a parallelogram are congruent.

2]m∠L = m∠N & m∠P = m∠MThus, The opposite angles of a parallelogram are congruent.

ML

NP