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Quadrilaterals Quiz - CBSE Class 8 Mathematics

Free practice quiz: Quadrilaterals (CBSE Class 8 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 17 multiple-choice questions on Quadrilaterals, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Angle Sum and Diagonals

A quadrilateral is a closed figure with four straight sides, four vertices and four angles.
Its interior angles always add to the same total, whatever its shape: trapezium, kite or parallelogram.
A diagonal joins two vertices that are not next to each other.

Interior angle sum of an n-sided polygon

\[(n-2)\times 180^\circ\]

Number of diagonals of an n-sided polygon

\[\frac{n(n-3)}{2}\]

Common mistake: Thinking the angle sum changes with the shape. It is the same for every quadrilateral, including trapeziums and kites.

Properties of a Parallelogram

A parallelogram has both pairs of opposite sides parallel. Its opposite sides are also equal.
Its opposite angles are equal, and any two adjacent angles add up to a straight angle.
Its diagonals bisect each other, meaning they cut each other into two equal halves.

Opposite angles in parallelogram ABCD

\[\angle A = \angle C,\; \angle B = \angle D\]

Adjacent angles are supplementary

\[\angle A + \angle B = 180^\circ\]

Opposite sides are equal

\[AB = CD,\; BC = AD\]

Common mistake: Assuming the diagonals of every parallelogram are equal. They only bisect each other. Equal diagonals happen only in rectangles and squares.

Rectangle, Rhombus and Square

A rectangle is a parallelogram with all right angles. Its diagonals are equal and bisect each other.
A rhombus is a parallelogram with all sides equal. Its diagonals are perpendicular bisectors of each other.
A square is both a rectangle and a rhombus. A parallelogram with one right angle or equal diagonals is a rectangle.

Rectangle ABCD: diagonals are equal

\[AC = BD\]

Rhombus: diagonals meet at right angles

\[AC \perp BD\]

Common mistake: Thinking a rhombus has equal diagonals or right angles. That is true only when the rhombus is also a square.

Trapezium and Kite

A trapezium has only one pair of parallel sides. A parallelogram has both pairs parallel.
A kite has two pairs of equal sides that are next to each other, not opposite each other.
In a kite, the diagonals are perpendicular, and one diagonal bisects the other.

Trapezium ABCD with AB parallel to DC

\[AB \parallel DC\]

Kite ABCD: equal adjacent sides

\[AB = AD,\; CB = CD\]

Common mistake: Calling a kite a parallelogram. In a kite the equal sides are adjacent, so opposite sides are usually not parallel.

Area of Common Quadrilaterals

Area measures the surface a shape covers. It is always written in square units, such as square centimetres.
For a parallelogram, use the base and the perpendicular height, not the slanting side.

Area of a rectangle (length l, breadth b)

\[A = l \times b\]

Area of a square (side a)

\[A = a^2\]

Area of a parallelogram (base b, height h)

\[A = b \times h\]

Common mistake: Mixing up area and perimeter, or writing area in plain units instead of square units.

Exam tips

Draw a quick sketch and mark the parallel and equal sides before choosing an answer.
Remember the family tree: every square is a rectangle and a rhombus, and all of these are parallelograms.
For NOT or TRUE questions, check each option against the shape's definition one by one.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the sum of the interior angles of a quadrilateral?
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Answer: A. 360 degrees
The sum of the interior angles of any quadrilateral is always 360 degrees. This is derived from the fact that a quadrilateral can be divided into two triangles, each having a sum of angles equal to 180 degrees.
In a parallelogram, opposite angles are:
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Answer: A. Equal
In a parallelogram, opposite angles are equal due to the properties of parallel lines and transversals.
Which property is true for all types of parallelograms?
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Answer: C. Opposite sides are equal
All parallelograms have the property that opposite sides are equal and parallel.
Which quadrilateral has diagonals that are perpendicular bisectors of each other?
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Answer: B. Rhombus
In a rhombus, the diagonals intersect at right angles and bisect each other, making them perpendicular bisectors.
If a square has a side length of 4 cm, what is its area?
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Answer: C. 16 cm²
The area of a square is calculated using the formula side × side. Therefore, 4 cm × 4 cm = 16 cm².