Question

Consider the figure and choose the correct option.

• A. ΔABC ≅ ΔDEF
• B. ΔABC ≅ ΔDFE
• C. ΔABC ≅ ΔFED
• D. ΔABC is not congruent to ΔFED

Answer 1

The correct option is C

ΔABC ≅ ΔFED

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)
So, ${180}^{\circ }$ - $\angle$ A - $\angle$ B = ${180}^{\circ }$ - $\angle$ F - $\angle$ E

$\Rightarrow$ $\angle$C = $\angle$D (Angle sum property of triangle)

$\angle$B = $\angle$E = ${90}^{\circ }$

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