Page 237 - Start Up Mathematics_8 (Non CCE)

15 Construction of Quadrilaterals

We have already learnt about construction of triangles in the previous class. A triangle consists of three sides
and three angles. To construct a triangle, we require three measures of sides or angles (with at least one given
side). A quadrilateral is a polygon with 4 sides, 4 enclosed angles and 2 diagonals. So, in all there are 10 building
blocks of a quadrilateral. Can you tell how many building blocks are required to draw a convex quadrilateral?

Construction of Quadrilaterals
To construct a convex quadrilateral, at least five building blocks are required.
In this chapter, we will learn to construct a convex quadrilateral with the following conditions:

(a) When the measures of 4 sides and 1 diagonal are given.
(b) When the measures of 3 sides and 2 diagonals are given.
(c) When the measures of 4 sides and 1 enclosed angle are given.
(d) When the measures of 3 sides and 2 enclosed angles are given.
(e) When the measures of 2 sides and 3 enclosed angles are given.

MATHS LAB ACTIVITY

Objective: To check the conditions of the construction of a quadrilateral
Material required: Cardboard strip (5 in number), pins (to make hinges),
a pair of scissors
Step 1: Take four cardboard strips of suitable lengths.
Step 2: With the help of pins, hinge the strips at the ends to form a
quadrilateral, as shown in the figure.
Step 3: Try to change the shape of the quadrilateral by pressing at
the opposite vertices. Isn’t it easy! This shows that different
quadrilaterals can be made from the same measure of the 4 sides.
Step 4: Add another strip in the form of a diagonal as shown in the figure.
Try to change the shape of the quadrilateral. If you observe carefully, now
it is not possible to do so.
Result: This shows that construction of a unique quadrilateral needs at least
5 building blocks (or dimensions). For example, 4 sides and 1 diagonal, etc.

P
Construction of Quadrilateral Given Its Four Sides and One Diagonal 4 cm 6 cm
Example 1: Construct a quadrilateral SKIP in which SK = 5.5 cm,
KI = 5 cm, IP = 6 cm, PS = 4 cm and diagonal S I
SI = 8 cm. 8 cm
Solution: Construction: First draw a rough sketch of the figure 5.5 cm 5 cm
to be constructed.
K