Question

From the figure given below, find the criteria of congruence followed by $\Delta ABC$ and $\Delta DEF$.

• A. S-A-S congruency
• B. A-S-A congruency
• C. A-A-S congruency
• D. Hypotenuse-leg congruency

Answer 1

The correct option is D Hypotenuse-leg congruency

From $\Delta ABC$ and $\Delta DEF$, we get:

BC = EF = 12 ft (given in the figure)

AC = DF = 13 ft (given in the figure)

$\angle ABC=\angle DEF$ ($\because \text{Right angles}$)

When the hypotenuse and one side of a right-angled triangle are congruent to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent by hypotenuse-leg congruency.

$\therefore \Delta ABC\cong \Delta DEF$ by hypotenuse-leg congruency.