Question

Which two triangles are congruent and by which congruent condition. ?

• A. $\Delta$ $\text{ABC}\cong$ $\Delta$ $\text{DEC}\left(\text{Hypotenuse Leg}\right)$
• B. $\Delta$ $\text{ABC}\cong$ $\Delta$ $\text{CED}\left(\text{SAS}\right)$
• C. $\Delta$ $\text{CAB}\cong$ $\Delta$ $\text{DEC}\left(\text{ASA}\right)$
• D. All are correct

Answer 1

The correct option is A $\Delta$ $\text{ABC}\cong$ $\Delta$ $\text{DEC}\left(\text{Hypotenuse Leg}\right)$

Here in the above picture,
$AB=DE\left(\text{given}\right)$

$\angle ABC=\angle DEC={90}^o\left(\text{given}\right)$

$AC=DC\left(\text{given}\right)$

Hence, $\Delta ABC\cong \Delta DEC\left(\text{Hypo. Leg. Cong.}\right)$

As, one of the sides and corresponding Hypotanuse are equal in the given right triangles, so congruence condition is Hypotenuse Leg Congruency.
Hence, option$\left(a\right)$ correct.