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