Quadrilaterals (चतुर्भुज) MCQ Test — Class 8 Maharashtra SSC

Solution:

A quadrilateral can be divided into two triangles by drawing one of its diagonals.

Since the sum of interior angles in each triangle is 180°, the sum of angles in the quadrilateral is the sum of angles of these two triangles.

Therefore, the sum of interior angles of a quadrilateral is 180° + 180° = 360°.

Solution:

A trapezium (or trapezoid) is defined as a quadrilateral with at least one pair of parallel sides.

In the CBSE/NCERT context for Class 8, it is typically understood as having exactly one pair of opposite sides parallel.

Options A, B, and D describe properties of other quadrilaterals like a rhombus, parallelogram, or general parallelogram, respectively.

Solution:

In a parallelogram, opposite sides are equal. So, AB = DC and AD = BC are correct statements.

In a parallelogram, opposite angles are equal. So, ∠A = ∠C is a correct statement.

The diagonals of a general parallelogram are not necessarily equal in length. They are equal only if the parallelogram is a rectangle or a square. Thus, AC = BD is a mistake for a general parallelogram.

Solution:

In a parallelogram, adjacent angles are supplementary, meaning their sum is 180°.

Angles P and Q are adjacent angles in parallelogram PQRS.

Therefore, ∠P + ∠Q = 180°.

Substituting the given value, 75° + ∠Q = 180°, which gives ∠Q = 180° - 75° = 105°.

Solution:

A key property of a parallelogram is that its diagonals bisect each other.

This means that the point of intersection (O) divides each diagonal into two equal parts.

So, for diagonal AC, the segments AO and OC must be equal (AO = OC).

Given AO = 5 cm, it directly follows that OC = 5 cm.

Solution:

A rhombus is a parallelogram with all four sides equal. A square is a parallelogram with all four sides equal AND all angles 90°.

Since a square has all four sides equal, it satisfies the definition of a rhombus. Thus, a square is always a rhombus.

A parallelogram does not necessarily have all sides equal (so A is false). A rectangle does not necessarily have all sides equal (so B is false). A trapezium only has one pair of parallel sides, not two pairs (so D is false).

Solution:

Properties A (opposite sides parallel), B (opposite angles equal), and C (diagonals bisect each other) are fundamental properties of *all* parallelograms.

A rectangle is defined as a parallelogram where all interior angles are right angles (90°). This is its distinguishing feature among parallelograms.

Solution:

Let the given angle be ∠A = 60°.

In a parallelogram, opposite angles are equal. So, the angle opposite to ∠A, let's say ∠C, will also be 60°.

Adjacent angles in a parallelogram are supplementary (their sum is 180°). So, ∠A + ∠B = 180°.

This means 60° + ∠B = 180°, so ∠B = 120°. The angle opposite to ∠B, let's say ∠D, will also be 120°.

Thus, the other three angles are 60°, 120°, and 120°.

Solution:

A quadrilateral with two distinct pairs of equal adjacent sides (AB=AD and CB=CD) is a kite.

One of the key properties of a kite is that its diagonals intersect at right angles.

Also, in a kite, only one of the diagonals is bisected by the other, and the diagonals are generally not equal in length.

Solution:

In a parallelogram, the diagonals bisect each other at their point of intersection (M).

This means M is the midpoint of diagonal EG, so EG is twice the length of EM. Given EM = 4 cm, EG = 2 × 4 cm = 8 cm.

Similarly, M is the midpoint of diagonal FH, so FH is twice the length of HM. Given HM = 3 cm, FH = 2 × 3 cm = 6 cm.

Therefore, the lengths are EG = 8 cm and FH = 6 cm.