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Understanding Elementary Shapes

    Angles – ‘Right’ and ‘Straight’

    Angles – ‘Acute’, ‘Obtuse’ and ‘Reflex’

    Exercise 5.7

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6th class > Understanding Elementary Shapes > Exercise 5.7

Exercise 5.7

1. Say True or False

Each angle of a rectangle is a right angle.
The opposite sides of a rectangle are equal in length.
The diagonals of a square are perpendicular to one another.
All the sides of a rhombus are of equal length.
All the sides of a parallelogram are of equal length.
The opposite sides of a trapezium are parallel.
True
False

2. Give reasons for the following :

(a)

A square can be thought of as a special rectangle.

Solution: A square can be considered a special because it meets all the criteria of a rectangle (four right angles, sides equal) but with the additional condition that all sides are equal.

This extra condition makes the square a more specific form of a .

(b)

(b) A rectangle can be thought of as a special parallelogram.

Solution: A rectangle can be considered a special because it meets all the criteria of a (opposite sides are equal in length and ) but with the additional condition that all four angles are angles.

This extra condition makes the a more specific form of a .

(c)

(c) A square can be thought of as a special rhombus.

Solution: A square can be considered a special because it meets all the criteria of a rhombus (all sides are equal in length, opposite sides are parallel, and opposite angles are ) but with the additional condition that all angles are angles.

This extra condition makes the square a more specific form of a .

(d)

(d) Squares, rectangles, parallelograms are all quadrilaterals.

Solution: Squares, rectangles, and parallelograms are all quadrilaterals because they all have sides, vertices, and angles.

They each have additional properties that classify them into more specific categories within the broader classification of quadrilaterals.

(e)

(e) Square is also a parallelogram.

Solution: A square meets all the criteria of a parallelogram: it has sides that are equal and parallel, its opposite angles are , and its diagonals bisect each other.

Additionally, a square has the extra properties that all sides are equal and all angles are angles.

Therefore, a square can be considered a special type of .

3. 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?

A regular figure that has its sides equal in length and angles equal in the measure is a .