Question

In ∆ABC and ∆DEF, it is given that ∠B = ∠E, ∠F = ∠C and AB = 3DE, then the two triangles are
(a) congruent but not similar
(b) similar but not congruent
(c) neither congruent nor similar
(d) similar as well as congruent

Answer 1

(b) similar but not congruent

In ∆ABC and ∆DEF, we have:
$$\begin{gathered} \angle B=\angle E\mathrm{and}\angle F=\angle C \\ \mathrm{Applying}AA\mathrm{similarity}\mathrm{theorem},\mathrm{we}\mathrm{conclude}\mathrm{that}△ABC~△DEF. \\ \mathrm{Also}, \\ AB=3DE \\ \Rightarrow AB\ne DE \\ \mathrm{Therefore},△ABC\mathrm{and}△DEF\mathrm{are}\mathrm{not}\mathrm{congruent}. \end{gathered}$$