Question

17.Prove that in a right triangle, the square of the hypotenuse is equal to the sum of squares of

the other two sides.

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Answer 1

Answer:

We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

We have,

△ADB∼△ABC. (by AA similarity)

Therefore, AD/AB=AB/AC

(In similar Triangles corresponding sides are proportional)

AB²=AD×AC……..(1)

Also, △BDC∼△ABC

Therefore, CD/BC=BC/AC

(in similar Triangles corresponding sides are proportional)

Or, BC²=CD×AC……..(2)

Adding the equations (1) and (2) we get,

AB²+BC²=AD×AC+CD×AC

AB²+BC²=AC(AD+CD)

( From the figure AD+CD=AC)

AB²+BC²=AC.AC

Therefore, AC²=AB²+BC²

This theorem is known as Pythagoras theorem

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