Question

5. In an equilateral triangle ABC, ADhypotenuse
BC, prove that ADsquare = 3 BDsquare​

Answer 1

Answer:

hy

Step-by-step explanation:

n an equilateral triangle ABC ,

AB = BC = AC

AD ⟂ BC

AD is also the perpendicular bisector of the side BC.

Hence, BD = DC

Also,

BC = 2 BD

According to Pythagoras theorem,

In ΔADB,

AB² = AD² + BD²

AD² = AB² - BD²

AB = BC ,

AD² = BC² - BD²

AD² = (2BD)² - BD²

AD² = 4BD² - BD²

AD² = 3BD²

hence Proved.