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In ΔABC and ΔDEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true? (A) not congruent and not similar (B) similar but not congruent (C) congruent and similar (D) none

Select the appropriate alternative.

In \(\triangle ABC\) and \(\triangle DEF\), \(\angle B = \angle E\), \(\angle F = \angle C\) and AB = 3DE then which of the statements regarding the two triangles is true?

(A) The triangles are not congruent and not similar (B) The triangles are similar but not congruent (C) The triangles are congruent and similar (D) None of the statements above is true.

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Answer: (B) The triangles are similar but not congruent.

\(\angle B = \angle E\) and \(\angle C = \angle F\), so by the AA test \(\triangle ABC \sim \triangle DEF\).

But AB = 3DE, so the corresponding sides are not equal (every side of \(\triangle ABC\) is 3 times the corresponding side of \(\triangle DEF\)). Hence the triangles are not congruent.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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