Question

Consider the figure and choose the correct option.

• A. $\Delta ABC\cong \Delta DEF$
• B. $\Delta ABC\cong \Delta DFE$
• C. $\Delta ABC\cong \Delta FED$​
• D. $\Delta ABC$ $≆$ $\Delta FED$​

Answer 1

The correct option is C

$\Delta ABC\cong \Delta FED$​

In $\Delta ABCand\Delta FED$

BC = ED (Given in the figure);
$\angle$ B = $\angle$ E = ${90}^{\circ }$
$\angle$ A = $\angle$ F (Given in the figure)
$\Rightarrow$ $\angle$C = $\angle$D (Angle sum property of triangle)

Therefore, by ASA congruence condition, $\Delta ABC\cong \Delta FED$ .