Question

In the given figure, AP = BP and CP = DP. Which of the following statements are true?

• A. $\angle CAP=\angle DBP$
• B. $\Delta APC\cong \Delta BPD$ by ASA postulate
• C. $AC\parallel BD$
• D. $\Delta APC\cong \Delta BPD$ by SAS postulate

Answer 1

Answer: (A), (C), (D)

$\Delta APC\cong \Delta BPD$ by SAS postulate

In $\Delta APC$ and $\Delta BPD$

(ii) $AP=BP$ …(given)

(ii) $\angle APC=\angle BPD$ ….(vertically opposite angles are equal

(iii) $CP=DP$ …(given)

$\therefore \Delta APC\cong \Delta BPD$ … (SAS postulate)

$\Rightarrow \angle CAP=\angle DBP$ ..(CPCT)

and $AC\parallel BD$ (alternate angles are equal)