SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 20 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Two right-angled triangular blocks, ABC and DEF, have ∠B=∠E=90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?

(a)Yes, by SSS
(b)Yes, by SAS
(c)Yes, by RHS
(d)Yes, by ASA

Answer

Why

Correct — C. Match what is given to a congruence rule.

∠B = ∠E = 90°: a right angle
AC = DF: the hypotenuse
AB = DE: one other side

Right angle, Hypotenuse, Side is the RHS rule, so the triangles are congruent → option (c)

Why the others are wrong

(a)
Yes, by SSS — SSS needs all three pairs of sides given. BC = EF is not given; it follows from Pythagoras, and RHS is the rule that packages exactly that step.
(b)
Yes, by SAS — SAS needs the angle between the two given sides. The right angle at B lies between AB and BC, not between AB and the hypotenuse AC.
(d)
Yes, by ASA — ASA needs two pairs of equal angles and the side between them. The data give one angle pair, ∠B = ∠E, plus two sides.

Concept

RHS (Right angle–Hypotenuse–Side): two right-angled triangles are congruent when the hypotenuse and one other side of one equal those of the other.

The given angle is not between the two given sides, so SAS cannot be applied straight away. The right angle is what makes it work: Pythagoras fixes the third side, BC = √(AC² − AB²) = √(DF² − DE²) = EF.

The standard congruence rules are SSS, SAS, ASA, AAS and RHS. AAA is not one of them: equal angles fix the shape of a triangle but not its size, so AAA gives similarity only.

Key facts

RHS: a right angle, the hypotenuse and one other side equal → the right triangles are congruent.
In SAS the equal angle must be the one included between the two equal sides.
Equal angles alone (AAA) prove similarity, not congruence.

Study next

SAS versus ASA: which angle or side is includedAAS: two angles and a non-included sideCorresponding parts of congruent triangles (CPCT)

Common traps

Choosing SAS because two sides and an angle are given, without checking that the angle lies between those sides.
Choosing SSS after computing BC = EF by Pythagoras — that side is derived, and the rule matching the given data is RHS.

The same 'are they congruent, and by what rule?' frame appears 19 Sep 2025, 16:00, Quant Q.20, where an angle bisector with AB = AC gives SAS, and 19 Sep 2025, 09:00, Quant Q.20, where a diagonal with AB = CD and ∠ABD = ∠CDB gives SAS.

10 Sep 2024, 09:00, Quant Q.3 turns it round: angle-angle-angle is the criterion that cannot prove congruence.

Related PYQs

No directly related past PYQ was found.

Topic: Congruence and similarity of triangles — all 25 SSC CGL questions on it, every solved shift.