Question

In the given figure, if AP = BP and DP = CP, then which of the following are true?

• A. $△PAD\cong △PBC$ by SAS postulate
• B. $△BAD\cong △ABC$ by SSS postulate
• C. $△BAD\cong △ABC$ by ASA postulate
• D. AP = AB

Answer 1

The correct option is A

$△PAD\cong △PBC$ by SAS postulate

In $△PAD$ and $△PBC$

(i) DP = CP .....(given)

(ii) $\angle DPA=\angle CPB$ ....(vertically opposite angles are equal )

(iii) AP = BP .....(given)

(iv) $△PAD\cong △PBC$ ......(SAS postulate)

(v) AD = BC ......(cpct)

Hence (A) and (D)