SSC CGL 2024 Tier-I · 9 September 2024, Shift 1 · Quantitative Aptitude · Question 5 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 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.

Which of the following statements is sufficient to conclude that two triangles are congruent?

(a)One side and one angle of both triangles are equal.
(b)These have two equal sides and the same perimeter.
(c)These have the same area and the same base.
(d)These have the same base and the same height.

Answer

Why

Correct — B. Two matching sides plus an equal perimeter force the third pair of sides to match too, which is SSS.

Let the triangles have sides a, b, c and a, b, f — two sides already agree.

Equal perimeters: a + b + c = a + b + f.
Cancel a + b: c = f.

All three pairs of sides are now equal, so the triangles are congruent by the side-side-side criterion — option (b).

Why the others are wrong

(a)
One side and one angle of both triangles are equal. — One side and one angle is only two elements, and every congruence test needs three. A 5 cm side with a 60° angle fits infinitely many differently shaped triangles.
(c)
These have the same area and the same base. — Equal area on an equal base fixes only the height. Slide the apex along a line parallel to the base and the area never moves while the other two sides change.
(d)
These have the same base and the same height. — Same base and same height gives equal areas and nothing more. A right triangle and an isosceles triangle can share a base and a height while their remaining sides differ.

Concept

Congruence needs three independent pieces of information in one of the standard patterns: SSS, SAS, ASA, AAS, and RHS for right triangles.

Area, perimeter and height are not on that list by themselves, because each is a single number that many different triangles share.

What makes the keyed option work is that the perimeter is not being used as a shape fact — it is arithmetic that recovers the missing third side, after which the ordinary SSS test applies.

SSA is deliberately absent from the list of criteria: two sides and a non-included angle can generate two different triangles, the ambiguous case.

Key facts

The valid congruence criteria are SSS, SAS, ASA, AAS and RHS.
Equal perimeter alone does not imply congruence, and neither does equal area.
Two equal sides plus an equal perimeter gives the third side by subtraction, completing SSS.

Study next

The similarity criteria AA, SSS and SAS, and how they differ from congruenceThe ambiguous SSA case and why it is not a congruence testRHS congruence for right-angled triangles

Common traps

Treating equal area as equal shape
Accepting AAA, which fixes the shape but not the size

This is a definition question dressed as a puzzle — no diagram, no numbers. The work is spotting which options supply only two facts, and which one quietly supplies a third.

Related PYQs

No directly related past PYQ was found.