Question

In the figure, altitudes $AD$ and $CE$ of $\Delta ABC$ intersect each other at the point P. Show that, $\Delta ABD~\Delta CBE$

Answer 1

Prove the given result based on the given information

We need to prove, $△ABD~△CBE$

Given that altitudes $AD$ and $CE$ of$\Delta ABC$ intersect each other at the point $P$

Consider $△ABD$ and $∆CBE$

$\angle ADB=\angle CEB$ [Each angle equal to $90°$]

$\angle ABD=\angle CBE$ [Common angle]

$\therefore$By AA (angle-angle) similarity criteria $∆ABD~△CBE$

Hence it is proved that $∆ABD~△CBE$