In triangles $ABC$ and $DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$. Which of the following makes the two triangles similar ?
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer
(b) ∠B = ∠D
Given $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, the sides AB, BC are about vertex B, and sides DE, FD are about vertex D. By SAS similarity criterion, the included angles must be equal, i.e., ∠B = ∠D.
Source: Chapter 6, Section 6.4 (SAS Similarity Criterion)
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Explanation
- The two given sides in △ABC are AB and BC — they include angle B.
- The two corresponding sides in △DEF are DE and FD — they include angle D.
- SAS similarity requires the included angle (between the two proportional sides) to be equal.
- ∠A and ∠F are not between those sides; ∠B = ∠E is not the right pairing (E is between DE and EF, but FD is given, not EF). Only ∠B = ∠D satisfies the SAS criterion here.