State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.
(A) In $\triangle ABC$ and $\triangle PQR$:
$\angle A = 60^{\circ}, \angle B = 80^{\circ}, \angle C = 40^{\circ}$
$\angle P = 60^{\circ}, \angle Q = 80^{\circ}, \angle R = 40^{\circ}$
Since $\angle A = \angle P = 60^{\circ}$,$\angle B = \angle Q = 80^{\circ}$,and $\angle C = \angle R = 40^{\circ}$,the corresponding angles are equal.
Therefore,by the $AAA$ (Angle-Angle-Angle) similarity criterion,$\triangle ABC \sim \triangle PQR$.
$\angle A = 60^{\circ}, \angle B = 80^{\circ}, \angle C = 40^{\circ}$
$\angle P = 60^{\circ}, \angle Q = 80^{\circ}, \angle R = 40^{\circ}$
Since $\angle A = \angle P = 60^{\circ}$,$\angle B = \angle Q = 80^{\circ}$,and $\angle C = \angle R = 40^{\circ}$,the corresponding angles are equal.
Therefore,by the $AAA$ (Angle-Angle-Angle) similarity criterion,$\triangle ABC \sim \triangle PQR$.
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