Question

State TRUE or FALSE

In a triangle ABC, right-angled at B, BD is drawn perpendicular to AC. hence, $\angle$ABD = $\angle$C

• A. True
• B. False

Answer 1

The correct option is A True

Given, $\angle ABC={90}^o$ and $\angle CDB={90}^o$
In $△ABC$,
$\angle BAC+\angle ABC+\angle ACB={180}^o$
$\angle BAC+\angle ACB+{90}^o={180}^o$
$\angle BAC+\angle ACB={90}^o$...(I)
In $△ABD$,
$\angle ABD+\angle ADB+\angle BAD=1806o$
$\angle ABD+\angle BAD+{90}^o={180}^o$
$\angle ABD+\angle BAD={90}^o$...(II)
Equating I and II
$\angle BAC+\angle ACB=\angle ABD+\angle BAD$
$\angle ACB=\angle ABD$ (Since, $\angle BAC=\angle BAD$)
$\therefore \angle ABD=\angle C$