# In $âˆ†ABC$, $\angle A=30^{\circ},\ \angle B=40^{\circ}$ and $\angle C=110^{\circ}$In $âˆ†PQR$, $\angle P=30^{\circ},\ \angle Q=40^{\circ}$ and $\angle R=110^{\circ}$. A student says that $âˆ†ABC ≅ âˆ†PQR$ by $AAA$ congruence criterion. Is he justified? Why or why not?

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No, because two triangles with equal corresponding angles need not be congruent. In such correspondence, one of them may be an enlarged copy of the other.

For example: Here are two triangles $∆ABC$, with $\angle A=30^{\circ},\ \angle B=40^{\circ}$ and $\angle C=110^{\circ}$

And $∆PQR$, $\angle P=30^{\circ},\ \angle Q=40^{\circ}$ and $\angle R=110^{\circ}$

But $∆ABC$ and $∆PQR$ both triangles are not congruent even though they have equal angles as shown in the figure below:

Updated on 10-Oct-2022 13:35:11