Question

In triangle ABC angle ACB is an obtuse angle seg AD perpendicular line BC then, show that : AB2 =BC2 +AC2 +2 BC. CD

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

In triangle ABD ,

DB =DC+BC--------- (1)

In triangle ADC,

AC^2=AD^2+DC^2

AC^2-DC^2=AD^2--------(2)

In triangle ADC,

BY PYTHAGORAS THEOREM ,

AB^2=AD^2+BD^2

AB^2=(AC^2-DC^2)+BD^2----(from 2)

AB^2=(AC^2-DC^2)+(DC+BC)^2(from1)

AB^2=AC^2-DC^2+DC^2+BC^2+2DC

×BC

AB^2=AC^2+BC^2+2BC×DC.

HENCE,PROVED.......

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