## Chapter 4 Practical Geometry Exercise 4.1

Question 1: Construct the following quadrilaterals.

i) Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

ii) Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

iii) Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Answer:

i)

Given

Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment AC = 7 cm.

2. With A as centre, radius 4.5 cm draw an arc.

3. With C as centre, radius 5.5 cm draw an arc to cut previous arc at B.

4. With A as centre and radius 6 cm draw an arc.

5. With C as centre and radius 4 cm draw an arc to cut previous arc at D.

6. Join, AB, BC, AD, CD.

7. ABCD is the required quadrilateral.

ii)

Given

Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment PU = 6.5 cm.

2. With P as centre, radius 4.5 cm draw an arc.

3. With U as centre, radius 3.5 cm draw an arc to cut the previous arc at J.

4. With P as centre, radius 5 cm draw an arc.

5. With U as centre, radius 4 cm, draw an arc to cut the previous arc at M.

6. Join JP, JU, PM, UM.

7. JUMP is the required quadrilateral.

iii)

Given

Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment EO = 7.5 cm.

2. With E as centre, radius 6 cm draw an arc.

3. With O as centre, radius 4.5 cm draw another arc to cut the previous arc at M.

4. With E as centre, radius 4.5 cm draw an arc.

5. With O as centre, radius 6 cm draw an arc to cut the previous arc at R.

6. Join ME, MO, ER, OR.

7. MORE is the required parallelogram.

iv)

Given

Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment TE = 6 cm.

2. With T as centre, radius 4.5 cm draw an arc.

3. With E as centre, radius 4.5 cm draw an arc to cut previous arc at B.

4. With T as centre, radius 4.5 cm draw an arc.

5. With E as centre, radius 4.5 cm draw an arc to cut the previous arc at S.

6. Join BT, BE, TS, ES.

7. BEST is the required rhombus.

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