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

Δ A P C ≅ Δ B P D

by ASA postulate

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Δ A P C ≅ Δ B P D

by SAS postulate

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∠ C A P = ∠ D B P

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A C ∥ B D

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Solution

The correct options are
B $Δ A P C ≅ Δ B P D$ by SAS postulate
C $∠ C A P = ∠ D B P$
D $A C ∥ B D$

In $Δ A P C$ and $Δ B P D$

(ii) $A P = B P$ …(given)

(ii) $∠ A P C = ∠ B P D$ ….(vertically opposite angles are equal

(iii) $C P = D P$ …(given)

$∴ Δ A P C ≅ Δ B P D$ … (SAS postulate)

$\Rightarrow ∠ C A P = ∠ D B P$ ..(CPCT)

and $A C ∥ B D$ (alternate angles are equal)

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