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If a quadrilateral is both a parallelogram and a kite, then it is a rhombus.

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Important Questions on Understanding Quadrilaterals

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then ∠A and ∠B respectively, are _____
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
In a square PQRS, if PQ=(2x+3) cm and QR=(3x-5) cm, then
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. The length of each side of the rhombus is 

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
The diagonals of a rhombus bisect each other at _____ angles.
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
Identify all the quadrilaterals that have four sides of equal lengths.
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

The diagonals of a rhombus are 16 cm and 12 cm. Find the length of each side of the rhombus.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
Atul is playing in a playground which is of the form of a parallelogram. He observes that the diagonals of the playground are 80 m and 60 m long. So, the playground can be the shape of _____.
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
The diagonals do not necessarily bisect the interior angle at the vertices in a 
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
The length of a rectangle is 8 cm and each of its diagonal measures 10 cm. The breadth of the rectangle is
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

Name the following parallelogram.

The diagonals are equal and the adjacent sides are unequal.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
In a rhombus, _____ angles are equal and all sides are equal.
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

Explain how a square is a quadrilateral.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
Prove that AC2+BD2=4AB2 in a rhombus ABCD.
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
The two diagonals are not necessarily equal in a
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

Prove that the diagonals of a rhombus bisect each other at right angles.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
ABCD is a rhombus with perimeter 24.8 cm . The length of each of its sides is:
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
In a square ABCD, AB=(2x+3) cm and BC=(3x-5) cm. Then, the value of x is
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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms

In the given figure, ABCD is a square. Find the measure of ∠CAD.

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Mathematics>Geometry>Understanding Quadrilaterals>Some Special Parallelograms
All the angles of a quadrilateral are equal to each other. Find the measure of each. Is the quadrilateral a parallelogram? What special type of parallelogram is it?