Question

Which of the following condition even if satisfied, does not make the two triangles congruent?

• A. S.S.S ( side-side-side)
• B. A.A.A (angle-angle-angle)
• C. S.A.S (side-angle-side)
• D. A.S.A (angle-side-angle)

Answer 1

The correct option is B A.A.A (angle-angle-angle)

Let us consider two triangles $\Delta ABC$ and $\Delta DEF,$
Clearly, $\angle A=\angle D,\angle B=\angle E$
and $\angle C=\angle F$ but
$AB\ne DE,BC\ne EF$ and $AC\ne DF$
$\therefore \Delta ABC$ is not congruent to $\Delta DEF.$
$\therefore$ $A.A.A$ condition even if satisfied does not make two triangles congruent.