Question

In the given figure, $AD=BC,AC=BD.$ Then $△PAB$ is

• A. equilateral
• B. right angled
• C. scalene
• D. isosceles

Answer 1

Answer: (D)

isosceles

In $△ADB$ and $△ACB$
$AD=BC$ (Given)
$AC=BD$
$AB=BA$ (Common)
$\therefore$ $△ADB\cong △ACB$ (SSS)
$\Rightarrow$ $\angle ABD=\angle CAB$ (cpct)
$\Rightarrow$ $\angle ABP=\angle PAB$
$\Rightarrow$ $PA=PB$ (Sides opp. equal angles are equal)
$\Rightarrow$ $△PAB$ is isosceles.