Question

Question 1 (vi)
State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Answer 1

(vi) $In\Delta DEF$,
we have,
$\angle D+\angle E+\angle F={180}^{\circ }$ (sum of all angles in a triangle is equal to ${180}^{\circ }$)
$\Rightarrow {70}^{\circ }+{80}^{\circ }+\angle F={180}^{\circ }$
$\Rightarrow \angle F={180}^{\circ }-{70}^{\circ }-{80}^{\circ }$
$\Rightarrow \angle F={30}^{\circ }$

$In\Delta PQR$,
we have,
$\angle P+\angle Q+\angle R={180}^{\circ }$ (sum of all angles in a triangle is equal to ${180}^{\circ }$)
$\Rightarrow \angle P+{80}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\Rightarrow \angle P={180}^{\circ }-{80}^{\circ }-{30}^{\circ }$
$\Rightarrow \angle P={70}^{\circ }$

$In\Delta DEFand\Delta PQR$,
we have,
$\angle D=\angle P={70}^{\circ }$
$\angle E=\angle Q={80}^{\circ }$
$\angle F=\angle R={30}^{\circ }$

$Hence,\Delta DEF\sim \Delta PQR\left(AAAsimilaritycriterion\right)$