Question

ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at p if ab is equal to BC prove that triangle ABC congruent to triangle PDC

Answer 1

Given: A cyclic quadrilateral ABCD in which AB = DC.
To prove: PAB  PDCProof: <BAC = <BDC [Angles in the same segment.]
Similarly, <ABD = <ACD [Angles in the same segment.]
In APB and PDC
AB = CD [Given]
<BAP = <CDP [From above]
<ABP = <DCP [From above]
Therefore, PAB  PDC