SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 2 of 100

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 5 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.

The points P and S are on the same side of the line segment QR, such that ∠PQR = 90°, ∠SRQ = 90° and PQ = SR. Select the correct statement.

Answer

Why

Correct — B. Read the vertices in the order the statement names them: ΔPQR ≅ ΔSRQ means P↔S, Q↔R, R↔Q.

Now test what that correspondence claims against what the question gives:
PQ = SR — given.
∠PQR = ∠SRQ = 90° — given, and it lies between the two named sides.
QR = RQ — the same segment.

Side, included angle, side. That is SAS → option (b).

Why the others are wrong

(a)
Right correspondence, wrong criterion. RHS needs the two hypotenuses equal — PR in ΔPQR against SQ in ΔSRQ — and the question never states that.
(c)
Wrong vertex order. ΔSQR pairs Q with Q and R with R, so it claims PQ = SQ and ∠PQR = ∠SQR — but the data give PQ = SR and ∠SRQ = 90°.
(d)
Two faults in one statement: the wrong correspondence of option (c), plus the unstated equal hypotenuses that sink option (a).

Concept

A congruence statement is an ordered claim, not just a pairing of two triangles.

Writing ΔPQR ≅ ΔSRQ asserts P↔S, Q↔R and R↔Q, and therefore that PQ = SR, QR = RQ and RP = QS. Change the letters to ΔSQR and you assert PQ = SQ instead — a different, and here false, statement about the same two triangles.

Only once the order is settled does the criterion matter, and it has to be justified by what is printed. SAS needs two sides with the angle between them; RHS needs a right angle, the hypotenuse and one leg.

Because PQ = SR and both stand perpendicular to QR on the same side, PQRS is a rectangle, so PR = SQ does in fact follow and RHS would then also work.

But that needs proving first. SSC keys the criterion the given data supply in one step, so read 'select the correct statement' as 'select the criterion that applies directly'.

Key facts

ΔPQR ≅ ΔSRQ asserts PQ = SR, QR = RQ and RP = QS, in that vertex order.
SAS requires the equal angle to lie between the two equal sides.
SSA, where the angle is not the included one, is not a congruence criterion.
RHS applies only to right triangles and needs the hypotenuse plus one leg — a shared right angle alone proves nothing.

Study next

The criteria SSS, SAS, ASA, AAS and RHS, and the exact data each one demandsWhy SSA fails, with the standard two-triangle counterexampleWriting a congruence statement in correct vertex order and reading off the CPCT consequences

Common traps

Checking the criterion but not the vertex order — ΔSQR and ΔSRQ are different claims.
Assuming RHS applies to any two right triangles that share a side.
Using QR = RQ silently and then forgetting to count it as the second side of SAS.

SSC prints a short set-up and four statements that differ only in vertex order or in the criterion named, so the mark turns on reading letters rather than on drawing. The same configuration returns as a CPCT follow-up asking for PR and SQ.

Related PYQs

No directly related past PYQ was found.