Question

$\text{In the given figure, DEFG is a square}\text{and}\angle BAC={90}^o.$


$\text{Which of the following is true?}$

• A. $△GAF\sim △DBG$
• B. $△AGF\sim △DBG$
• C. $△FGA\sim △EFC$
• D. $△AGF\sim △EFC$

Answer 1

Answer: (B), (D)

The correct options are
B $△AGF\sim △DBG$
D $△AGF\sim △EFC$

$\text{Since DEFG is a square,}GF||DE||BC.$

$\text{In}△AGF\text{and}△DBG,\text{we have}\angle GAF=\angle BDG={90}^o$

$\text{and,}\angle AGF=\angle DBG\text{(Since corresponding angles are equal)}$

$\therefore △AGF\sim △DBG\text{(By AA similarity criterion)}$

$\text{In}△AGF\text{and}△EFC$,
$\angle FAG=\angle CEF={90}^o$

$\text{and}\angle AFG=\angle ECF$
$\text{(Since corresponding angles are equal)}$

$\therefore △AGF\sim △EFC\text{(By AA similarity criterion)}$