In △ABC and △DEF, if AB = EF, BC = DE and CA = FD, then
Correct Answer :
△ABC ≅ △FED
Solution :
The correct option is △ABC ≅ △FED.
To determine the correct congruence relation between the two triangles, we must match the corresponding vertices based on the given equal side lengths:
1. We are given that AB = EF.
This means side AB corresponds to side EF.
2. We are given that BC = DE.
This means side BC corresponds to side DE.
3. We are given that CA = FD.
This means side CA corresponds to side FD.
Now, let us trace the correspondence of the vertices:
- Vertex A corresponds to vertex F (since AB = FE and CA = FD, vertex A is common to AB and CA, and vertex F is common to FE and FD).
- Vertex B corresponds to vertex E (since AB = FE and BC = ED, vertex B is common to AB and BC, and vertex E is common to FE and ED).
- Vertex C corresponds to vertex D (since BC = ED and CA = FD, vertex C is common to BC and CA, and vertex D is common to ED and FD).
Therefore, by the Side-Side-Side (SSS) congruence criterion, triangle ABC is congruent to triangle FED:
Hence, △ABC ≅ △FED is the correct congruent statement.
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