**Practical Geometry**

**Question 1.****Draw the following:**

**Solution.**

Draw a rough sketch of the required square and write down its dimensions.*Steps of Construction :*

- Draw RE = 5.1 cm.
- DrawRX ⊥RE.
- With R as centre and radius 5.1 cm, draw an arc to cut RX at D.
- With D as centre and radius 5.1 cm, draw an arc.
- With E as centre and radius 5.1 cm, draw another arc cutting the previous arc at A.
- Join DA and EA.

Then, READ is the required square.

**Question 2.****A rhombus whose diagonals are 5.2 cm and 6.4 cm long.**

**Solution:**

Let diagonal AC = 5.2 cm and diagonal BD = 6.4 cm.

Draw AC = 5.2 cm. Draw XY, the perpendicular bisector of AC which cuts AC at 0.

With O as centre, draw arcs of radii which

cut OX at D and OY at B.

Join AB, BC, CD and DA.

Then, ABCD is the required rhombus.

**Question 3.****A rectangle with adjacent sides of lengths 5 cm and 4 cm.**

**Solution:**

We know that the opposite sides of a Y 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 = 5 cm. 5cm
- Draw ∠OKX = 90°.
- With K as centre and radius 4 cm, draw an arc KX at A.
- With A as centre and radius 5 cm, draw an arc.
- With O as centre and radius 4 cm, draw another arc cutting the previous arc at Y.
- Join AY and OY.

Then, OKAY is the required rectangle.

**Question 4.****A parallelogram OKAY where OK = 5.5 cm and KA = 42 cm.**

**Solution:**

In order to draw a quadrilateral, we need five measurements.

But here to draw the parallelogram OKAY, we are given two consecutive sides, i.e., four sides (the opposite sides being equal). So, we need information about one of its elements more. It may be the included angle between the sides or one of the diagonals to construct a unique quadrilateral. So, the required parallelogram cannot be drawn.