How to prove AB is not equal to BC

Question

IS there any way to prove AB is not equal to BC? the figure is drawn to scale. And this is a gre question.

Answer 1

B could be on the Thales circle over AC, and AB need not be equal to BC.

One method to check whether AB : BC is the same proportion as CD : DA could be to draw a line between B and D. If the line crosses the line AC in the middle, the proportion is the same. Otherwise not.

Bye

See also: Thales theorem

Answer 2

Hint: $\angle DAB$ need not be right.

Pun intended.