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Question 1. Asked on :01 March 2019:03:26:35 PM

#### How to prove Pythagorus theorem .

-Added by Akki chauhan Mathematics » Maths

Himanshi Verma

ABC is a right angle triangle at B and BD is a perpendicular from B on to AC, the diagonal.

Triangles ABC and BDC are similar, as:

. angle DBC = 90 - angle C = angle A

. angle ABC = angle BDC = 90

Ratios of corresponding sides are equal.

AB / BD = BC / DC = AC / BC

So we get  BC² = AC * DC     --- (1)

Triangle ABC amd ADB are similar, as:

. angle DBA = 90 - (90 - C) = angle C

. angle ABC = 90 = angle ADB

so ratios of corresponding sides are equal

AB / AD = BC / BD = AC / AB

So we get  AB² = AD * AC  --- (2)

Add (1) and (2) to get:

AB² + BC² = AC * ( AD + DC) = AC * AC = AC²

So the theorem is proved.

-Answered by Himanshi Verma On 01 March 2019:03:38:26 PM(1378Average Rating Based on rating)

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