Question

In the given figure, $△$ $ABC$ is right angled at $B$. If $BD$ $\perp$ $AC$, which of the following is/are true?

• A. $△$ $ABC$ $\sim$ $△$ $ADB$
• B. $△$ $ABC$ $\sim$ $△$ $BDC$
• C. $△$ $ADB$ $\sim$ $△$ $BDC$
• D. $△$ $ABC$ $\sim$ $△$ $DBC$

Answer 1

Answer: (A)

$△$ $ABC$ $\sim$ $△$ $ADB$

In $△ABC$ and $△ABD$, we have

$\frac{AB}{AC}=\frac{BD}{BC}$

And $\angle ADB=\angle ABC=90$

$△ABC$ and $△ADB$ are similar.

Similar $ABC$ and $BDC$ are similar.