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
Solution:
(b) similar but not congruent
In ∆ABC and ∆DEF, we have:
$\angle B=\angle E$ and $\angle F=\angle C$
Applying $A A$ similarity theorem, we conclude that $\triangle A B C \sim \triangle D E F$.
Also,
$A B=3 D E$
$\Rightarrow A B \neq D E$
Therefore, $\triangle A B C$ and $\triangle D E F$ are not congruent.
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