Page 190 - ICSE Math 8

THINK SMART

1. How many triangles are formed by drawing diagonals from a vertex of the following polygons?
(a) Pentagon (b) Hexegon (c) Octagon (d) Decagon
Also, find the measure of each angle of all the polygons. 4 4

2. The side length of the original tangram is 8 units. Find the area of each of
the smaller shapes of the tangram. 4

8
4

8
Maths Lab Activity

Objective: To verify that the sum of the interior angles of a quadrilateral is 360º
Material required: Coloured paper (2 different colours), sketch pen, geometry box, a pair of scissors,
glue stick/fevicol
Step 1: Draw a quadrilateral on a paper, say light blue, and cut it [Fig. (i)].
Step 2: Draw and cut another quadrilateral of the same size on a different paper, say dark blue.
Step 3: Paste the light blue quadrilateral in your notebook.

Step 4: Now cut the corners of the dark blue quadrilateral [as shown in the Fig. (ii)] along the dotted
lines.
Step 5: Paste the remaining dark blue quadrilateral on the light blue quadrilateral so that the corresponding
sides overlap as shown in Fig. (iii).

3 3
2 2

1 4 1 4
(i) (ii) (iii)

Step 6: Now paste the cut-out vertices so that the tips meet each other
[Fig. (iv)].
Observation:

Note that when all the angles are joined together, we get a complete angle, 2 3
i.e., a circle. 1 4
∴ ∠1 + ∠2 + ∠3 + ∠4 = 360º

Result: The sum of all the interior angles of a quadrilateral is 360º.

(iv)

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