Quadrilaterals & Special Quadrilaterals Quiz - ICSE Class 8 Mathematics
Free practice quiz: Quadrilaterals & Special Quadrilaterals (ICSE Class 8 Mathematics). 42 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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In a parallelogram ABCD, if $\angle A = 70^\circ$, then the measure of $\angle B$ is:
- $70^\circ$
- $110^\circ$
- $90^\circ$
- $180^\circ$
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Answer: B. $110^\circ$
In a parallelogram, consecutive angles are supplementary. Therefore, $\angle A + \angle B = 180^\circ$. Given $\angle A = 70^\circ$, we have $70^\circ + \angle B = 180^\circ$, which means $\angle B = 180^\circ - 70^\circ = 110^\circ$.
A kite has diagonals of length 8 cm and 6 cm. What is its area?
- $24$ cm$^2$
- $48$ cm$^2$
- $14$ cm$^2$
- $28$ cm$^2$
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Answer: A. $24$ cm$^2$
The area of a kite is given by the formula $\frac{1}{2} imes d_1 imes d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. Here, $d_1 = 8$ cm and $d_2 = 6$ cm. So, Area = $\frac{1}{2} imes 8 imes 6 = \frac{1}{2} imes 48 = 24$ cm$^2$.
If a parallelogram has diagonals that are equal in length and bisect each other at right angles, then the parallelogram must be a:
- Rectangle
- Rhombus
- Square
- Kite
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Answer: C. Square
A parallelogram with equal diagonals is a rectangle. A parallelogram with diagonals that bisect each other at right angles is a rhombus. A parallelogram that is both a rectangle and a rhombus is a square. Therefore, a parallelogram with diagonals that are equal, bisect each other, and are perpendicular must be a square.
A quadrilateral ABCD has angles $\angle A = 90^\circ$, $\angle B = 90^\circ$, $\angle C = 120^\circ$, and $\angle D = 60^\circ$. This quadrilateral is a:
- Rectangle
- Rhombus
- Trapezoid
- Square
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Answer: C. Trapezoid
The sum of interior angles is $90^\circ + 90^\circ + 120^\circ + 60^\circ = 360^\circ$, which is correct for a quadrilateral. For it to be a trapezoid, at least one pair of opposite sides must be parallel. If $\angle B = 90^\circ$ and $\angle C = 120^\circ$, then $\angle B + \angle C = 210^\circ$, so BC is not parallel to AD. If $\angle A = 90^\circ$ and $\angle D = 60^\circ$, then $\angle A + \angle D = 150^\circ$, so AB is not parallel to DC. However, if $\angle A = 90^\circ$ and $\angle B = 90^\circ$, this means that AD is parallel to BC because the angles on the same leg (AB) are supplementary (which is not the case here, $90+90=180$). Wait, angles on the same leg being supplementary implies the other two sides are parallel. If $\angle A = 90^\circ$ and $\angle B = 90^\circ$, then AD is parallel to BC. Therefore, it is a trapezoid. It is not a rectangle because $\angle C$ and $\angle D$ are not $90^\circ$. It is not a rhombus because not all sides are necessarily equal, and angles are not all equal. It is not a square as it's not a rectangle with equal sides.
What is the sum of the interior angles of a quadrilateral formed by joining the midpoints of the sides of a larger square?
- $180^\circ$
- $360^\circ$
- $270^\circ$
- $90^\circ$
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Answer: B. $360^\circ$
Connecting the midpoints of the sides of a square forms another square inside it. Let the vertices of the outer square be (0,a), (a,a), (a,0), (0,0). The midpoints are (a/2, a), (a, a/2), (a/2, 0), (0, a/2). These four midpoints form a square. A square is a quadrilateral. The sum of the interior angles of any quadrilateral is $360^\circ$.