Question

In the given figure, $AP=DP$, $\angle A=\angle D$ and $\angle B=\angle C={90}^o$
which of the following is correct

• A. $P$ is the mid-point of $BC$
• B. $△ABP\cong △DCP$
• C. $AB=DC$
• D. $AB=PB$

Answer 1

Answer: (A), (B), (C)

$AB=DC$

In triangles $△ABP$ and $△DCP$
$\angle B=\angle C$ (given)
$\angle A=\angle D$ (given)
$AP=DP$ (given)
Hence, $△ABP\cong △DCP$ (AAS)
So,
$BP=CP$ (C.P.C.T)
so, $P$ is the mid-point of $BC$
Also, $AB=DC$ (C.P.C.T)
Hence, option $\left(a\right)$, $\left(b\right)$ and $\left(c\right)$ are correct.