Question

ABC is an equalliteral triangle if d is midpoint then prove that4 ad square = 3bc square

Answer 1

Answer:

Given : ABC is an equalliteral triangle if D is midpoint then BD = CD

And AB = BC = AC

To prove : 4AD² + 3BC

Step-by-step explanation:

In ΔABD, by pythagoreas theorem

AB²= AD² + BD²    .........(1)

In ΔADC

AC²= AD² + DC²   ...........(2)

From (1) and (2) , we get

AB²+AC²= 2AD²+ BC²+ DC²

AB²+ AC²= 2AD²+ (BD²+DC²) + (AC²- AD²)

AB²+AC²=2AD²+BD²+DC²+AC²+AD²