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.
(N/A) In $\Delta DEF$,the sum of angles is $180^{\circ}$.
Given $\angle D = 70^{\circ}$ and $\angle E = 80^{\circ}$.
Therefore,$\angle F = 180^{\circ} - (70^{\circ} + 80^{\circ}) = 180^{\circ} - 150^{\circ} = 30^{\circ}$.
In $\Delta PQR$,the sum of angles is $180^{\circ}$.
Given $\angle Q = 80^{\circ}$ and $\angle R = 30^{\circ}$.
Therefore,$\angle P = 180^{\circ} - (80^{\circ} + 30^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}$.
Comparing the two triangles:
$\angle D = \angle P = 70^{\circ}$
$\angle E = \angle Q = 80^{\circ}$
$\angle F = \angle R = 30^{\circ}$
Since all corresponding angles are equal,by the $AAA$ (Angle-Angle-Angle) similarity criterion,the triangles are similar.
Symbolic form: $\Delta DEF \sim \Delta PQR$.
Given $\angle D = 70^{\circ}$ and $\angle E = 80^{\circ}$.
Therefore,$\angle F = 180^{\circ} - (70^{\circ} + 80^{\circ}) = 180^{\circ} - 150^{\circ} = 30^{\circ}$.
In $\Delta PQR$,the sum of angles is $180^{\circ}$.
Given $\angle Q = 80^{\circ}$ and $\angle R = 30^{\circ}$.
Therefore,$\angle P = 180^{\circ} - (80^{\circ} + 30^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}$.
Comparing the two triangles:
$\angle D = \angle P = 70^{\circ}$
$\angle E = \angle Q = 80^{\circ}$
$\angle F = \angle R = 30^{\circ}$
Since all corresponding angles are equal,by the $AAA$ (Angle-Angle-Angle) similarity criterion,the triangles are similar.
Symbolic form: $\Delta DEF \sim \Delta PQR$.
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