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There are various types of quadrilaterals. They are:
• Square
• Rectangle
• Parallelogram
• Trapezium
• Rhombus
• Kite
A square is a quadrilateral with four equal sides and four right angles.

A square has:
• four equal sides $$AB=BC=CD=DA$$.
• four right angles $$∠A=∠B=∠C=∠D=90°$$.
• two pairs of parallel sides $$AB∥DC$$  and $$AD∥BC$$.
• two equal diagonals $$AC=BD$$.
• diagonals that are perpendicular to each other $$AC⊥BD$$.
• diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.
A rectangle is a quadrilateral with two pairs of equal and parallel opposite sides and four right angles.

A rectangle has:
• two pairs of parallel sides $$AB∥DC$$ and $$AD∥BC$$.
• four right angles $$∠A=∠B=∠C=∠D=90°$$.
• opposite sides of equal lengths $$AB=DC$$ and $$AD=BC$$
• two equal diagonals $$AC=BD$$
• diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

A parallelogram has:
• two pairs of parallel sides $$PQ∥RT$$ and $$PR∥QT$$.
• opposite sides of equal lengths $$PQ=RT$$ and $$PR=QT$$.
• opposite angles that are equal $$∠P=∠T$$ and $$∠Q=∠R$$.
• two diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.
A trapezium is a quadrilateral in which one pair of opposite sides is parallel.
• The sides that are parallel to each other are called bases.
In the above figure, $$EF$$ and $$GH$$ are bases.
• The sides that are not parallel to each other are called legs.
In the above figure, $$EG$$ and $$FH$$ are legs.

There is nothing special about the sides, angles, or diagonals of a trapezium.

But if the two non-parallel opposite sides are of equal length, then it is called an isosceles trapezium.

The above quadrilateral $$XYZW$$ is an isosceles trapezium.

In an isosceles trapezium, the lengths of the diagonals are equal. That is $$XZ=WY$$.

A rhombus is a quadrilateral with four equal sides.
A rhombus has:
• two pairs of parallel sides $$EH∥FG$$ and $$EF∥HG$$.
• four equal sides $$EH=HG=GF=FE$$.
• opposite angles are equal $$∠E=∠G$$ and $$∠H=∠F$$.
• diagonals that are perpendicular to each other $$EG⊥HF$$.
• diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.
A kite is a quadrilateral in which two pairs of adjacent sides are equal.
A kite has:
• two pairs of equal adjacent sides $$AB=BC$$ and $$CD=DA$$.
• one pair of opposite angles (which are obtuse) that are equal $$∠A=∠C$$
• diagonals that are perpendicular to each other $$AC⊥BD$$
• a longer diagonal that bisects the shorter diagonal.
The following chart allows us to understand the hierarchy of quadrilaterals.