8th Maths 4.5

Chapter 4

Practical Geometry

NCERT Class 8th Solution of Exercise 4.1

NCERT Class 8th Solution of Exercise 4.2

NCERT Class 8th Solution of Exercise 4.3

NCERT Class 8th Solution of Exercise 4.4

EXERCISE 4.5

Draw the following.
1. The square READ with RE=5.1 cm.
2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
4. A parallelogram OKAY where OK = 5.5 cm and KA=4.2 cm. Is it unique?

`text{Solution:}`
1. `text{The square READ with RE=5.1 cm.}`

`text{Rough sketch of a parallelogram READ.}`

`text{Fair sketch of a parallelogram READ.}`

`text{Step of construction.}`

1) `text{Draw RE=5.1 cm.}`

2) `text{Draw an angle of 90° at E and cut}``text{ EA=5.1 cm.}`

3) `text{Draw two arcs from A and R with a}``text{ radius of 5.1 cm intersect at D.}`

4) `text{Join AD and RD.}` 

5) `text{We get rhombus READ.}`

2.`text{A rhombus whose diagonals are 5.2 cm}``text{ and 6.4 cm long.}`

`text{Rough sketch of a parallelogram ABCD.}`

`text{Fair sketch of a parallelogram ABCD.}`

`text{Step of Construction:}`

`[text{Diagonal of a rhombus bisect each other at}``text{ the right angle.}]`

1) `text{Draw AC = 5.2 cm.}`

2) `text{Draw perpendicular bisector of AC at O.}`

3) `text{Draw two arcs with a center}``text{ O of radius }``1/2text{×DE =}``1/2text{×6.4 = 3.2 cm}``text{ to meet the perpendicular bisector at B}``text{ and D.}` 

5) `text{Join AB, BC, CD, and DA}`

6) `text{We get rhombus ABCD.}`

3. `text{A rectangle with adjacent sides of}``text{ lengths 5 cm and 4 cm.}`

`text{Rough sketch of a rectangle ABCD.}`

`text{Fair sketch of a rectangle ABCD.}`

`text{Step of construction}`

`[text{Each angle of a rectangle is 90° and}``text{ opposite sides are equal.}]`

1) `text{Draw AB=5 cm.}`

2) `text{Draw an angle of 90° at B and}``text{ cut BC=4 cm.}`

3) `text{Draw an arc with center C of radius 5 cm.}`

4) `text{Draw another arc with a center A of radius}``text{ 4 cm to meet the previous arc at D.}`

5) `text{Join BC, CD and DA.}`

6) `text{We get rectangle ABCD.}`

4. `text{A parallelogram OKAY where}``text{ OK = 5.5 cm and KA=4.2 cm.}``text{ Is it unique?}`

`text{Rough sketch of a parallelogram OKAY.}`

`text{Fair sketch of a parallelogram OKAY.}`

`text{Step of Construction:}`

`[text{Opposite sides of a parallelogram are equal.}]`

1) `text{Draw OK = 5.5 cm.}`

2) `text{Draw an angle 60° at K of and}``text{ cut KA 4.2 cm.}`

3) `text{Draw an arc with a center A of radius}``text{ 5.5 cm.}`

4) `text{Draw another arc with a center O of}``text{ radius 4.2 cm to meet the previous arc}``text{ at Y.}`

5) `text{Join AY, and OY}`

6) `text{We get quadrilateral OKAY}`

`text{No, it is not a unique parallelogram}``text{ because value of angle K can other than 60°}`