Types of quadrilaterals
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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