Question

In the given figure, P is the midpoint of AB. If $\angle PAC=\angle PBD,$ then which of the following are true?

• A. $△APC\cong △BPD$ by SAS postulate
• B. $△APC\cong △BPD$ by SSS postulate
• C. $△APC\cong △BPD$ ASA postulate
• D. P is midpoint of CD

Answer 1

Answer: (C), (D)

The correct options are
C

$△APC\cong △BPD$ ASA postulate

D

P is midpoint of CD

In $△APC$ and $△BPD$,

(i) $\angle PAC=\angle PBD$ .....(given)

(ii) AP = BP ......(given, P is midpoint of AB)

(iii) $\angle APC=\angle BPD$ ......(vertically opposite angles)

(iv) $△APC\cong △BPD$....(ASA Postulate)

(v) CP = DP .....(cpct)

Hence, P is the midpoint of CD

Hence (C) and (D)