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Alternate Proof of Pythagoras Property
The Pythagoras property can also 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:

4 cm
5 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.

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