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# 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?

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:

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