ex 17c class 6 icse math

1. Name each shape:

Shapes and Their Names

2. Fill in the blanks:

(i) A quadrilateral with all sides and all angles equal is a square.
(ii) A quadrilateral with four equal sides and no right angles can be called a rhombus.
(iii) A quadrilateral with exactly two sides parallel is a trapezium.
(iv) The diagonals of this quadrilateral are equal but not perpendicular. The quadrilateral is a rectangle.

3. Determine if the given statements are sometimes, always, or never true:

(i) A parallelogram is a quadrilateral. → Always true
(ii) A rhombus is a square. → Sometimes true (only if all angles are 90°)
(iii) A rectangle is a square. → Sometimes true (only if all sides are equal)
(iv) A square is a rectangle. → Always true
(v) A parallelogram is a trapezium. → Sometimes true (only if it has one pair of parallel sides)
(vi) A trapezium is a quadrilateral. → Always true
(vii) A square is a rhombus. → Always true
(viii) Four-sided plane figures are parallelograms. → Sometimes true (only if both pairs of opposite sides are parallel)

4. Write 'T' for True or 'F' for False:

(i) Each angle of a rectangle is a right angle. → T
(ii) The opposite sides of a rectangle are equal in length. → T
(iii) The diagonals of a square are perpendicular to one another. → T
(iv) The diagonals of a rhombus are of equal length. → F (They are perpendicular but not necessarily equal unless it's a square)
(v) All the sides of a rhombus are of equal length. → T
(vi) All the sides of a parallelogram are of equal length. → F (Only opposite sides are equal)
(vii) The opposite sides of a trapezium are parallel. → F (Only one pair of sides is parallel)

5. Give reasons for the following:

(i) A square can be thought of as a special rectangle. Reason: A square has all the properties of a rectangle (four right angles, opposite sides equal and parallel) and also has all sides equal.
(ii) A rectangle can be thought of as a special parallelogram. Reason: A rectangle has all the properties of a parallelogram (opposite sides equal and parallel) and also has all angles equal to 90°.
(iii) A square can be thought of as a special rhombus. Reason: A square has all the properties of a rhombus (all sides equal, opposite sides parallel) and also has all angles equal to 90°.
(iv) Squares, rectangles, parallelograms are all quadrilaterals. Reason: All these shapes have four sides, making them quadrilaterals.
(v) Square is also a parallelogram. Reason: A square has both pairs of opposite sides parallel and equal, which is a property of parallelograms.

6. Multiple Choice Questions (MCQs):

A quadrilateral whose diagonals are equal and bisect each other at right angles is a: (d) Square
A quadrilateral-shaped photo-frame has all sides equal. Which of the following is not a possible shape for the photo-frame? (b) Rectangle (A rectangle does not necessarily have all sides equal)
A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral? (c) Square
Which quadrilateral is not a parallelogram? (b) Trapezium (A trapezium has only one pair of parallel sides, while a parallelogram has two pairs)

Sushovan Pal