Chapter 13. Quadrilaterals NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 13. Quadrilaterals | NIOS Class 10 Mathematics Important Questions, Fully Solved Answers, and Chapter-wise Exam Preparation Guide.

Chapter 13. QUADRILATERALS

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

Short Questions and Answers for Algebraic Expressions and Polynomials [1 or 2 Marks]

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 13.1

1. Name each of the following quadrilaterals.

Photo  Fig. 13.10

Answer: (i) Rectangle   (ii) Trapezium   (iii) Rectangle   (iv) Parallelogram   (v) Rhombus   (vi) Square

2. State which of the following statements are correct ?

(i) Sum of interior angles of a quadrilateral is 360°.

(ii) All rectangles are squares,

(iii) A rectangle is a parallelogram.

(iv) A square is a rhombus.

(v) A rhombus is a parallelogram.

(vi) A square is a parallelogram.

(vii) A parallelogram is a rhombus.

(viii) A trapezium is a parallelogram.

(ix) A trapezium is a rectangle.

(x) A parallelogram is a trapezium.

Answer: (i) Sum of interior angles of a quadrilateral is 360°. →True
[ This is a fundamental property of all quadrilaterals.]

(ii) All rectangles are squares. → False .
[ A rectangle has opposite sides equal, but a square has all four sides equal. Only some rectangles are squares. ]

(iii) A rectangle is a parallelogram. → True .
[ A rectangle has both pairs of opposite sides parallel, so it is a parallelogram.]

(iv) A square is a rhombus. → True
[ A square has all sides equal, so it satisfies the definition of a rhombus.]

(v) A rhombus is a parallelogram. → True
[ A rhombus has both pairs of opposite sides parallel, so it is a parallelogram.]

(vi) A square is a parallelogram. → True
[ A square has both pairs of opposite sides parallel, so it is a parallelogram.]

(vii) A parallelogram is a rhombus. → False
[ A parallelogram does not necessarily have all sides equal (only opposite sides are equal). Only some parallelograms are rhombuses.]

(viii) A trapezium is a parallelogram. →False
[ A trapezium has only one pair of opposite sides parallel, whereas a parallelogram has two pairs.]

(ix) A trapezium is a rectangle. → False
[ A rectangle has two pairs of parallel sides and right angles, while a trapezium has only one pair of parallel sides.]

(x) A parallelogram is a trapezium. → False
[ A trapezium is defined as a quadrilateral with at least one pair of opposite sides parallel. Since a parallelogram has two pairs.]

 

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