Question

If $AD$ and $BC$ are both perpendicular to $AB$, and $BD=AC$, then $\Delta ABC$ is congruent to

• A. $\Delta BAD$
• B. $\Delta ADB$
• C. $\Delta BAD\&\Delta ADB$

Answer 1

The correct option is A $\Delta BAD$

here, we have given $AD$ and $BC$ perpendicular to $AB$
And, $BD=AC$.
$\therefore$ Using Hyptenuese Leg Theorem:
$\Delta ABC\cong \Delta BAD$
Now, we also need to check if $\Delta ABC\cong \Delta ADB$
We need to check if $AB=AD$ or $AC=AB$ or $BC=DB$.
Well, if we look at the 2nd condition that is $AC=AB$, we notice that it's not possible as $AC$ is the hypotenuse of the $\Delta ABC$, and $AB$ is one of the legs.
$\Rightarrow AC>AB$
Which is not satisfied.
Hence $\Delta ABC$ is not congruent to $\Delta ADB$