Question

In given figure $ABC$ is a triangle in which altitudes $BD$ and $CE$ to sides $AC$ and $AB$ are equal Show that
$△ABD\cong △ACE$

Answer 1

Given ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal

In $\Delta ADB$ and $\Delta ACE$

$\angle ADB=\angle AEC={90}^0$ (altitudes BD and CE to sides AC and AB)

$BD=CE$ (Given altitudes are equal

$\angle BAD=\angle DAB$ (Common angle )

$\Delta ABD\cong \Delta ACE$ .....(SAA test)