Question

prove that triangle ABC is right angled at A. ​

Answer 1

Answer:hello....Sol: ln ΔABC, AD⊥BC, so. ΔABD AB2 = AD2 + BD2 --------------- (1) [Pythagoras theorem] ΔACD AC2 = AD2 + CD2 --------------- (2) [Pythagoras theorem]

Adding equations (1) and (2),

AB2 + AC2 = AD2 + BD2 + AD2 + CD2

AB2 + AC2= 2AD2 + BD2 + CD2 AB2+AC2 = 2×BD×CD +BD2+CD2

[Given that AD2=BD×CD]

AB2 + AC2 = (BD + CD)

[ 2ab+ a2+b2= (a+b)2]

AB2 + AC2 = BC2 [BD+CD=AD]

hence⇒ΔABC is a right angled triangle.

hence prove

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