**Practical Geometry**

**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

**Solution.****(i)** First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown.

We may divide it into two conveniently constructible As ABC and ACD.

*Steps of Construction :*- Draw AC = 7 cm.
- With A as centre and radius 4.5 cm, draw an arc (below AC).
- With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.
- Join AB and BC.
- With A as centre and radius 6 cm, draw an arc (above AC).
- With C as centre and radius 4 cm, draw another arc cutting the previous arc at D.
- Join AD and CD.

Then, ABCD is the required quadrilateral.

**(ii)** First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.

We may divide it into two conveniently constructible As PJU and PMU.*Steps of Construction :*

- Draw PU = 6.5 cm.
- With P as centre and radius 4.5 cm, draw an arc (below PU).
- With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.
- Join PJ and JU.
- With P as centre and radius 5 cm, draw an arc (above PU).
- With U as centre and radius 4 cm, draw another me cutting the previous arc at M.
- Join PM and UM.

Then, JUMP is the required quadrilateral.

**(iii)** Draw a rough sketch of the’ required parallelogram and write down the given dimensions.*Steps of Construction :*

- Draw OR = 6 cm.
- With O as centre and radius 7.5 cm, draw an arc.
- With R as centre and radius 4.5 cm, draw another arc to cut the previous arc at E.
- Join OE and RE.
- With 0 as centre and radius 4 5 cm 4.5 cm, draw an arc.
- With E as centre and radius 6 cm, draw another arc to cut the previous arc at M.
- Join MO and ME.

Then, MORE is the required parallelogram.

**(iv)** Draw a rough sketch of the required rhombus and write down the given dimensions.*Steps of Construction :*

- Draw BE = 4.5 cm.
- With B as centre and radius 4.5 cm, draw an arc. 4 5 cm
- With E as centre and radius 6 cm, draw another arc to cut the previous arc at T.
- Join ST and ET.
- With T as centre and radius 4.5 cm, draw an arc.
- With E as centre and radius 4.5 cm, draw another arc to cut the previous arc at S.
- Join TS and ES.

Then, BEST is the required rhombus.