question_answer

ABCD is a quadrilateral such that BC = BA and CD > AD. Which one of the following is correct?

A) \[\angle BAD\text{ }=\angle BCD\]

B) \[\angle BAD<\angle BCD\]

C) \[\angle BAD>\angle BCD\]

D) \[2\angle BAD=\angle BCD\]

Correct Answer: C

Solution :

Join AC. 7 Now, in \[\Delta ABC\], \[~\therefore AB=BC\therefore \angle ~BAC-\angle BCA\]... (i) (angles opposite to equal side) In \[\Delta ADC,~\therefore CD>AD\] \[\therefore \]   \[\therefore \angle DAC\text{ }>\angle DCA\]               ...(ii) (since, in a triangle, angle opposite to greater side is bigger than the angle opposite to smaller side) On adding Eqs. (i) and (ii), we get\[\angle BAD>\angle BCD\]