Page 181 - ICSE Math 7

Verification of pythagoras property

The Pythagoras property can be verified using graph paper. Let’s take a right-angled triangle with
sides 3 cm, 4 cm and 5 cm as shown. Cut squares of sides 3 cm, 4 cm and 5 cm from a graph sheet.
Paste the squares obtained from the graph sheet as shown below:

5 cm
4 cm
3 cm

2
The number of unit squares in the square formed on the hypotenuse is 5 , i.e., 25.
2
The number of unit squares in the square formed on the base is 3 , i.e., 9.
2
The number of unit squares in the square formed on the perpendicular is 4 , i.e., 16.
Since the number of squares on the hypotenuse (i.e., 25) is equal to the sum of the squares formed on
the other two sides (i.e., 9 + 16).

Hence, Pythagoras property is verified.

Converse of pythagoras property

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then
the triangle is right-angled and the angle opposite to the first side, i.e., the greatest side is a right
angle.

Pythagorean triplet

If the square of the longest side of a triangle is equal to the sum of the squares of the remaining two
sides, then the measures of the sides of such a triangle are known as Pythagorean triplet. For example,
(3, 4, 5), (6, 8, 10) and (5, 12, 13) are Pythagorean triplets.

Example 5: Find the unknown length x in the following figures.

10 cm x 10 cm 10 cm
6 cm

x
8 cm
(a) (b)

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