# Understanding Quadrilaterals

## Exercise 3.4

1). State whether True or False.

(a) All rectangles are squares

(b) All rhombuses are parallelograms

(c) All squares are rhombuses and also rectangles

(d) All squares are not parallelograms.

(e) All kites are rhombuses.

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.

Answer:

(a) All rectangles are squares

Ans: False

(b) All rhombuses are parallelograms

Ans: True

(c) All squares are rhombuses and also rectangles

Ans: True

(d) All squares are not parallelograms.

Ans: False

(e) All kites are rhombuses.

Ans: False

(f) All rhombuses are kites.

Ans: True

(g) All parallelograms are trapeziums.

Ans: True

(h) All squares are trapeziums.

Ans: True

2). Identify all the quadrilaterals that have.

(a) four sides of equal length (b) four right angles

Solution:

(a) four sides of equal length

Ans: Rhombus, square.

(b) four right angles

Ans: Rectangle, square.

3). Explain how a square is.

(i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle

Solution:

(i) a quadrilateral

Ans: A square has four sides. Therefore, it is a quadrilateral.

(ii) a parallelogram

Ans: Opposite sides of a square are parallel to each other. Therefore, it is a parallelogram.

(iii) a rhombus

Ans: A square is a parallelogram with all four sides equal. Therefore, it is a rhombus.

(iv) a rectangle

Ans: A square is a parallelogram with each angle being a right angle. Therefore, it is a rectangle.

4). Name the quadrilaterals whose diagonals.

(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal

Solution:

(i) bisect each other

Ans: Parallelogram. rectangle, rhombus, square.

(ii) are perpendicular bisectors of each other

Ans: Rhombus, square.

(iii) are equal

Ans: Square, rectangle.

5). Explain why a rectangle is a convex quadrilateral.

Ans: Both the diagonals of a rectangle lie in it’s interior. Therefore, it is a convex quadrilateral.

6). ABC is a right-angled triangle and O is the midpoint of the side

opposite to the right angle. Explain why O is equidistant from A,

B and C. (The dotted lines are drawn additionally to help you).

In the □ABCD opposite sides are parallel.

Therefore, □ABCD is a parallelogram.

Diagonals of parallelogram bisect each other.

Hence, O is equidistant from A, B and C.

Click here for the solutions of Std 8 Maths

1). Rational Numbers

2). Linear Equations in One Variable

3). Understanding Quadrilaterals

4). Data Handling