8th Math 3.4

NCERT Class 8th solution of Exercise 3.1

NCERT Class 8th solution of Exercise 3.2

NCERT Class 8th solution of Exercise 3.3

Exercise 3.4

Q1. 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.

`text{Answer:}`

a) `text{false,}` b) `text{true,}` c) `text{true,}` d) `text{false,}` e) `text{false,}` f) `text{true,}` g) `text{true,}` h) `text{true.}` 

Q2. Identify all the quadrilaterals that have.

a) four sides of equal length

b) four right angles

`text{Answer:}`

a) `text{Rhombus, Square}`    

b) `text{Square, Rectangle}`

Q3. Explain how a square is.

i) a quadrilateral

ii) a parallelogram

iii) a rhombus

iv) a rectangle

`text{Answer:}`

i) `text{A square is 4 - sided; so it is a quadrilateral.}`

ii) `text{A square has its opposite sides parallel; }`

`text{so it is a parallelogram.}`

iii) `text{A square is a parallelogram with all the 4 sides}`

`text{equal; so it is a rhombus.}`

iv) `text{A square is a parallelogram with each angle a }`

`text{right angle; so it is a rectangle.}`

Q4. Name the quadrilaterals whose diagonals.

i) bisect each other

ii) are perpendicular bisectors of each other

iii) are equal

`text{Answer:}`

i) `text{Parallelogram; Rhombus; Square; Rectangle.}`

ii) `text{Rhombus; Square}`

iii) `text{Square; Rectangle}`

Q5. Explain why a rectangle is a convex quadrilateral.

`text{Answer:}`

`text{Both of it diagonals lie in its interior.}`

Q6. `text{ABC}` is a right-angled triangle and `text{O}` is the mid point of the side opposite to the right angle. Explain why `text{O}` is equidistant from `text{A, B}` and `text{C}`. (The dotted lines are drawn additionally to help you).

`text{Answer:}`

`overline text{AD}∥ overline text{BC}; overline text{AB} ∥ overline text{DC}`. `text{So, in parallelogram ABCD, the mid-point}` `text{if diagonal } overline text{AC}text{ is O}.`