If ad is perpendicular to BC in a triangle ABC D then prove that a b square + CD square is equal to BD square + AC square
Answers
Answered by
4
ABD is a right angled traingle
and AB is the hypotaneous
(AB)^2 = (AD)^2 + (BD)^2
(AB)^2 - (BD)^2 = (AD)^2 ---------(i)
now,
ACD is also a right angled traingle
(AC)^2 = (AD)^2 + (DC)^2
(AC)^2 - (DC)^2 = (AD)^2 ----------(ii)
(i) = (ii)
(AB)^2 - (BD)^2 =(AC)^2 - (DC)^2
(AB)^2 +(DC)^2 = (AC)^2 + (BD)^2
and AB is the hypotaneous
(AB)^2 = (AD)^2 + (BD)^2
(AB)^2 - (BD)^2 = (AD)^2 ---------(i)
now,
ACD is also a right angled traingle
(AC)^2 = (AD)^2 + (DC)^2
(AC)^2 - (DC)^2 = (AD)^2 ----------(ii)
(i) = (ii)
(AB)^2 - (BD)^2 =(AC)^2 - (DC)^2
(AB)^2 +(DC)^2 = (AC)^2 + (BD)^2
Similar questions