exam

Given: AF = CD = BF

To prove: AB = BC= CA

Proof:

Consider BDC and EBC

BC = BC (common)

BD = BE (altitudes are equal)

BDC = EBC = 90⁰    (altitude)

By RHS BDC EBC

ABC = ACB

⇒ AB = AC.......(1)

Similarly we can prove that

BC = AC.......(2)

and there by from (1) & (2)

AB = BC = AC

Hence the ABC is an equilateral triangle.