Q.3 - Exercise 18.2 - Chapter 18 - Practical Geometry (Construction of Quadrilaterals) RD Sharma 8
Channel: Math Solutions Foundation
Date: 29/10/2021

In this video, question 3 from exercise 18.2 RD Sharma Class 8 which is based on the topic constructing a quadrilateral when four sides  and one diagonal are given. This question is from the book R D Sharma Class 8 from chapter 18 Practical Geometry (Constructions) 
3. Construct a quadrilateral ABCD, when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm. 
Introduction
In earlier classes, we have learnt about the construction of triangles. We have seen that to construct a triangle we require three measurements of sides or angles (at least one of them is a side). Now a natural question arises whether four measurements would be sufficient to draw a quadrilateral. In fact a quadrilateral has 10 elements (four sides, four angles and two diagonals) and to draw a quadrilateral nay five independent elements must be given. In this chapter, we will study construction of quadrilaterals.
Construction of Quadrilaterals
As we know that the shape and size of a polygon are defined by its elements. The elements that make a polygon are its sides, enclosed angles and diagonals. A triangle is the simplest polygon. It does not have any diagonal. So, the elements that define a triangle are its three sides and three angles. It is possible to draw a triangle if the size of any three independent elements are given. In the previous class, we have learnt how to construct a triangle when:
(i) its three sides are given;
(ii) its two sides and the angle included side are given;
(iii) its two angles and the included side are given;
(iv) the hypotenuse and one side of a right triangle are given.
In case of a quadrilateral the elements are its four sides, two diagonals and its four angles. Thus, a quadrilateral has ten elements. It is possible to draw a convex quadrilateral if any five independent elements are given. To draw a non=convex quadrilateral, six independent elements are required. 
In what follows, we shall learn to construct a convex quadrilateral in the following simple cases:
(i) when the lengths of four sides and one diagonal are given;
(ii) When the lengths of three sides and the two diagonals are given;
(iii) when the lengths of four sides and one angle are given;
(iv) when the lengths of three sides and two included angles are given;
(v) when three angles and two included sides are given.
Constructing a quadrilateral when four sides and one diagonal are given
When four sides and a diagonal of a quadrilateral are given, we consider the quadrilateral ABCD as a figure made of two triangles:
(i) Triangle ABC and ADC when diagonal AC as the common side is given
or (ii) triangle ABD and BCD when diagonal BD as the common side is given.
In order to draw the quadrilateral when four sides and one diagonal are given, we first draw a rough sketch of the quadrilateral and write its dimensions along the sides and then we divide it into two conveniently constructable triangles.
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