In a right triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides​

2 thoughts on “In a right triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides​”

1. Answer:

   Check your answer please

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2. Step-by-step explanation:

   Given:

   A right angled ∆ABC, right angled at B

   To Prove- AC²=AB²+BC²

   Construction: draw perpendicular BD onto the side AC .

   Proof:

   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 theroem is known as Pythagoras theroem…

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