Question Details

In △ABC and △DEF, if AB = EF, BC = DE and CA = FD, then

Options

A

△ABC ≅ △DEF

B

△ABC ≅ △FED

C

△ABC ≅ △EFD

D

△ABC ≅ △DFE

Show Answer

Correct Answer :

Option B

△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:

ABC FED

Hence, △ABC ≅ △FED is the correct congruent statement.

Unlock Our Free Library

Access expert-curated educational resources and study materials—completely free.

Discover more resources

You may also like

Mock Tests

View All
  • CLAT
  • intermediate
  • 2 hours
  • current affairs, general knowledge, legal reasoning, logical reasoning, quant

  • CLAT
  • intermediate
  • 2 hours
  • current affairs, english, general knowledge, legal reasoning, logical reasoning, quant

Ask AI Tutor
5 left
Q1 View Question & Options
AI Tutor is solving this question...
Reading question context & options...