# Excercise 4.4 Practical Geometry- NCERT Solutions Class 8

## Chapter 4 Ex.4.4 Question 1

Construct the following quadrilaterals.

(i) Quadrilateral $$DEAR$$

$$DE = 4\,\rm{cm}$$

$$EA = 5\,\rm{cm}$$

$$AR = 4.5\,\rm{cm}$$

$$\angle E = 60^\circ$$

$$\angle A = 90^\circ$$

(ii) Quadrilateral $$TRUE$$

$$TR = 3.5\,\rm{cm}$$

$$RU = 3\,\rm{cm }$$

$$UE = 4\,\rm{cm}$$

$$\angle R = 75^\circ$$

$$\angle U=120^\circ$$

### Solution

What is known?

Measurements of a Quadrilateral ($$3$$ line segments and $$2$$ angles).

What is unknown?

Construction of a Quadrilateral

Reasoning:

As you are aware, we need five measurements to draw a quadrilateral. The given measurements are of three sides and two included angles (Page 58 of Grade 8 NCERT Book)

Steps:

Let us draw a rough diagram with the given measurements to find out whether it is possible to construct a quadrilateral

Let us construct the quadrilateral

Step 1: Draw a line segment $$TR = 3.5\,\rm{cm.}$$

Step 2: With $$R$$ as center construct an angle of  $$75^\circ.$$  With $$R$$ as center and radius $$3\,\rm{cm}$$ draw an arc cutting the ray from $$R$$ at $$U.$$

Step 3: With $$U$$ as center construct an angle of $$120^\circ.$$  With $$U$$ as center and radius $$4\,\rm{cm}$$ draw an arc cutting the ray from $$U$$ at $$E.$$

Step 4: Join $$TE.$$

Step 5: $$TRUE$$ is the required quadrilateral.

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