Question

In the given figure, AC = BD. Prove that AB = CD.

Answer 1

From the given figure, we have:
AC = AB + BC
BD = BC + CD
It is given that AC = BD.

Therefore, AB + BC = BC + CD..................(1)
According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal.
Subtracting BC from both sides in equation (1), we get:
AB + BC- BC = BC + CD - BC
AB = CD
Hence proved.