Extra Questions: Class 8 Maths Chapter 4 Quadrilaterals

Practice questions beyond the textbook exercises, testing deeper understanding of quadrilateral properties for Class 8 Maths Chapter 4: Quadrilaterals. These Class 8 Mathematics Chapter 4 important questions are handy for last-minute exam practice.

Extra Questions: Class 8 Maths Chapter 4 Quadrilaterals

1. 1 (Assertion-Reason). Assertion: Every square is a rhombus. Reason: A square has all four sides equal.
   Solution: Both true, and the reason correctly explains the assertion — a rhombus is defined as a parallelogram with all sides equal, which a square satisfies.
2. 2 (Numerical). In a parallelogram, one angle is 65°. Find all four angles.
   Solution: Opposite angles are equal and co-interior angles sum to 180°: 65°, 115°, 65°, 115°.
3. 3 (Synthesis). Can a trapezium have three right angles? Explain.
   Solution: No — three right angles would force the fourth to also be 90° (angle sum 360°), making it a rectangle, which has two pairs of parallel sides, not the trapezium’s single pair.
4. 4 (Applied). The diagonals of a rhombus are 6 cm and 8 cm. Find the length of each side.
   Solution: Diagonals bisect each other at right angles, giving half-diagonals 3 cm and 4 cm; by Pythagoras, side = √(3²+4²) = √25 = 5 cm.
5. 5 (Assertion-Reason). Assertion: A kite’s diagonals are always equal. Reason: A kite has two pairs of adjacent equal sides.
   Solution: Assertion is false (kite diagonals are generally unequal); reason is true but doesn’t support a false assertion — so the correct response is that the assertion is false.
6. 6 (Numerical). Three angles of a quadrilateral are 80°, 95°, and 100°. Find the fourth.
   Solution: 360−(80+95+100) = 85°.
7. 7 (Short Answer). Name the quadrilateral whose diagonals are equal, bisect each other, and are also perpendicular.
   Solution: Square.
8. 8 (Synthesis). If both pairs of opposite angles of a quadrilateral are equal, what can you conclude about its sides?
   Solution: It must be a parallelogram, so both pairs of opposite sides are equal and parallel.
9. 9 (Applied). ABCD is a parallelogram with ∠A=70°. Find ∠B, ∠C, ∠D.
   Solution: ∠B=110° (co-interior), ∠C=70° (opposite to A), ∠D=110° (opposite to B).
10. 10 (Assertion-Reason). Assertion: An isosceles trapezium’s base angles are equal. Reason: Its non-parallel sides (legs) are equal in length.
    Solution: Both true, and the reason correctly explains the assertion — equal legs in an isosceles trapezium produce equal base angles on each parallel side.

Written by Satish

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