Question

Show that in two triangles $\Delta$ABC and $\Delta$DEF, whether in the following conditions they are similar or not. Why?
(i) $\angle A={30}^o,\angle B={50}^o,\angle C={80}^o$
(ii) $\angle D={50}^o,\angle E={30}^o,\angle F={80}^o$.

Answer 1

In $\Delta$ABC
$\angle A+\angle B+\angle C={30}^o+{50}^o+{80}^o={160}^o$
In $\Delta$ DEF
$\angle D+\angle E+\angle F={50}^o+{30}^o+{80}^o={160}^o$
We know that the sum of three angles of a triangle is ${180}^o$
$\therefore$ $\Delta$ABC and $\Delta$ DEF are not possible.
$\angle A\ne \angle D,\angle B\ne \angle E,\angle C=\angle F$.
$\because$ All the corresponding angles are not equal, the triangles ABC and DEF are not similar.