Pythagoras Theorem Proof - satveeracademy

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Right angled Triangle:-

A triangle in which one of the angles measures 90 ⁰is called a right angled triangle or simply right triangle.

observe figure ABC is a right angle triangle at Angle B opposite side of right angle is biggest side AC is the longest side, it is called “hypotenuse”.

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

Given :

ABC is a right triangle, right angle at B

RTP : AC ² = AB² + BC²

Construction : Draw BD perpendicular to AC.

Proof :

In ∆ ADB and ∆ABC

∠A= ∠A

∠ADB= ∠ABC= 90 ⁰

By AA similarity property

∆ADB~ ∆ABC

sides are proportional

Similarly in ∆ BDC and ∆ABC

∠C= ∠C

∠BDC= ∠***ABC*= 90 ⁰**

By AA similarity property

∆BDC ~ ∆ABC

sides are proportional

Hence proved

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