**Question 1: **

**Construct the following quadrilaterals. **

**i) Quadrilateral of PQRS**

**PQ = 4.5 cm **

**QR = 5.5 cm**

**RS =4 cm **

**PS = 6 cm **

**PR =7 cm **

**ii) Quadrilateral of HUMP **

**HU = 3.5 cm **

**UM =4cm **

**MP = 5 cm **

**PH = 4.5 cm**

**PU = 6.5 cm **

**iii) Parallelogram of CORE **

**OR = 6 cm **

**RE = 4.5 cm **

**E0 = 7.5 cm**

**iv) Rhombus of WEST**

**WE=4.5cm**

**ET=6cm**

**Answer:**

i) Firstly , a rough sketch of this quadrilateral can be drawn as follows:

1.

2. Vertex S is 6cm away from vertex P. Therefore, while taking P as centre, drawn an arc of radius 6cm.

3. Taking R as centre, draw an arc of radius 4cm, cutting the previous arc at point S. Join S to and R.

PQRS is the required quadrilateral.

**(ii) Firstly, a rough sketch of this quadrilateral can be drawn as follows. **

(1)

(2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M.

(3) Join M to P and U.

JUMP is the required quadrilateral.

**(iii)We know that opposite sides of a parallelogram are equal in length and also these are parallel to each other**.

Hence, CE = OR, CO = ER

A rough sketch of this parallelogram can be drawn as follows.

(1)

(2) Vertex M is 4.5 cm away from vertex 0 and 6 cm away from vertex E. Therefore, while taking 0 and E as centres, draw arcs of 4.5 cm radius and 6cm radius respectively. These will intersect each other at point M.

(3) Join C to 0 and E.

CORE is the required parallelogram.

**(iv)We know that all sides of a rhombus are of the same measure. **

Hence, WE = ES = ST = TW

A rough sketch of this rhombus can be drawn as follows.

(1)

(2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will be intersecting each other at point S.

( 3 ) Join S to E and T.

WEST is the required rhombus.