SSC CGL 2024 Tier-I · 12 September 2024, Shift 1 · Quantitative Aptitude · Question 17 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

In triangles ABC and DEF, AB = FD and ∠ A = ∠ D. The two triangles are congruent by SAS criterion if:

(a)AC = DE
(b)AC = EF
(c)BC = DE
(d)BC = EF

Answer

Why

Correct — A. In SAS the equal angle must sit between the two pairs of equal sides.

Given: AB = FD and ∠A = ∠D.

In △ABC the arms of ∠A are AB and AC.
In △DEF the arms of ∠D are DF and DE.

AB = FD already pairs AB with DF, so the arms still unmatched are AC and DE. SAS closes when AC = DE → option (a).

That fixes the correspondence A ↔ D, B ↔ F, C ↔ E, so the congruence is written △ABC ≅ △DFE.

Why the others are wrong

(b)
AC = EF — EF is opposite ∠D, not an arm of it. Pairing AC with EF leaves one arm of ∠D unmatched, so the given angle stops being the included angle.
(c)
BC = DE — BC is opposite ∠A while DE is an arm of ∠D. The two are not corresponding parts under any reading, so this pairs nothing.
(d)
BC = EF — BC and EF are both opposite the given angles. Added to AB = FD that gives two sides and a non-included angle — the SSA pattern, which does not prove congruence.

Concept

SAS is an ordered criterion: side, included angle, side. The angle must be the one formed by the two pairs of equal sides, and an angle anywhere else in the triangle will not do.

So the question reduces to naming the arms. ∠A is contained by AB and AC; ∠D is contained by DF and DE.

One pair of arms, AB and FD, is already given equal. Congruence therefore needs the remaining pair, AC and DE.

Correspondence is decided by the letters, not by the triangle names: AB = FD says B answers to F, which leaves C answering to E.

The stem writes AB = FD, not AB = DE, and that reversal is the whole question. Read the vertex letters in the order the paper prints them rather than assuming ABC lines up with DEF.

Key facts

SAS requires the equal angle to be the angle contained by the two pairs of equal sides.
The arms of ∠A in △ABC are AB and AC.
The arms of ∠D in △DEF are DE and DF.
AB = FD makes A correspond to D and B to F, leaving C to correspond to E.

Study next

SSS, ASA, AAS and RHS, and why AAA and SSA are not criteriaWriting a congruence statement in the correct vertex orderCPCT — deducing the remaining sides and angles once congruence is established

Common traps

Reading the correspondence as A ↔ D, B ↔ E, C ↔ F, which contradicts the given AB = FD.
Choosing a side opposite the given angle instead of an arm of it.
Treating SSA, two sides and a non-included angle, as a congruence criterion.

SSC tests the congruence criteria two ways — as a definition question about which criterion works, and as a correspondence question where the vertex letters are deliberately scrambled.

Also asked 10 Sep 2024, 09:00, Quant Q.3, which asks which criterion cannot prove congruence, and 11 Sep 2024, 12:30, Quant Q.14, where △ABC ≅ △RPQ and you must name the side of △ABC that matches PQ.

Related PYQs

No directly related past PYQ was found.