**Practical Geometry**

**Question 1.****Construct the following quadrilaterals :**

**(i) Quadrilateral MORE**

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

**(ii) Quadrilateral PLAN**

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N – 85°.

**(iii) Parallelogram HEAR**

HE = 5 cm

EA = 6 cm

∠R = 85°

**(iv) Rectangle OKAY**

OK = 7 cm

KA = 5 cm.

**Solution.****(i)** Draw a rough sketch of the required quadrilateral and write down its dimensions.*Steps of Construction :*

- Draw MO = 6 cm.
- Make ∠MOX = 105°.
- With O as centre and radius 4.5 cm, cut off OR = 4.5 cm along OX.
- Make ∠ORY = 105°.
- Make ∠ZMO = 60° such that arms RY and MZ intersect at E.

Then, MORE is the required quadrilateral.

**(ii)** Draw a rough sketch of the required quadrilateral PLAN and write down its dimensions.

Before taking up the construction let us find the ∠PLA which is equal to 360° – (90°+ 110°+ 85°)

= 360°-285° = 75°.**Steps of Construction :**

- Draw PL = 4 cm.
- Make ∠XPL =90°.
- Make ∠YLP = 75°.
- With L as centre and radius 6.5 cm, cut off LA – 6.5 cm along LY.
- Make ∠ZAL =110° and let its arm AZ intersect PX at N.

Then, PLAN is the required quadrilateral.

**(iii)** We know that the opposite angles of a parallelogram are equal. Make a rough sketch of the required parallelogram as shown.**Steps of Construction :**

- Draw HE = 5 cm.
- Make ∠HEX = 85°.
- With E as centre and radius 6 cm, cut off EA = 6 cm along EX.
- With A as centre and radius 5 cm, draw an arc.
- With H as centre and radius 6 cm, draw another arc cutting the previous arc at R.
- Join HR and AR.

Then, HEAR is the required parallelogram.

**(iv)** We known that the opposite sides of a rectangle are equal and each angle of it is 90°.

Make a rough sketch of the required

rectangle and write down its dimensions.**Steps of Construction :**

- Draw OK = 7 cm.
- Draw ∠OKX = 90°.
- With K as centre and radius 5 cm, draw an arc KX at A.
- With A as centre and radius 7 cm, draw an arc.
- With O as centre and radius 5 cm, draw another arc cutting the previous arc at Y.
- Join AY and OY.

Then, OKAY is the required rectangle.