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Maths

Triangles

Pythagoras Theorem and its Converse

Prove that, in a right-angl...

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Asked on October 15, 2019 by

Rion Chris

Prove that, in a right-angled triangle, the square of hypotenuse is equal to the sum of the square of remaining two sides.

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ANSWER

Consider a right angled triangle with length of hypotenuse as c and the remaining two sides as a and b respectively.

We arrange 4 such triangles in such a fashion that they form a square of side a+b (as shown in the figure).

Area of the figure A= (a+b)(a+b) .......(1)

Also area of the figure can be written as, A=4×ar(Bluerighttriangle)+ar(centralyellowsquare)

A=4×

2

1

ab+c

2

.......(2)

Equating (1) and (2) we get,

c

2

+2ab=a

2

+b

2

+2ab

Consequently, c

2

=a

2

+b

2

. Hence, Pythagoras theorem is proved.