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