SSC CGL 2025 Tier-I · 19 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 11 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.

In a quadrilateral ABCD, a line segment BD is a diagonal such that AB=CD and ∠ABD=∠CDB. Are the triangles ABD and CDB congruent? If so, by what rule?

(a)Yes, by SSS
(b)Yes, by SAS
(c)Yes, by ASA
(d)No, they are not congruent

Answer

Why

Correct — B.
Match the vertices: A ↔ C, B ↔ D, D ↔ B.

Side: AB = CD (given)
Angle: ∠ABD = ∠CDB (given), each lying between that side and BD
Side: BD = DB (common to both triangles)

Two sides and the angle included between them → SAS → option (b)

Why the others are wrong

(a)
Yes, by SSS — SSS needs AD = CB as a third pair of sides, and the stem does not give it. AD = CB follows only after the SAS congruence is proved.
(c)
Yes, by ASA — ASA needs two pairs of equal angles with the side between them. The stem gives one angle pair, ∠ABD = ∠CDB, so ASA cannot be applied from the data.
(d)
No, they are not congruent — They are congruent: AB = CD, ∠ABD = ∠CDB and the shared side BD make a complete SAS set. Nothing the criterion needs is missing.

Concept

SAS proves two triangles congruent when two sides and the angle between them match. The angle must be the included one: two sides and a non-included angle (SSA) do not guarantee congruence.

In a quadrilateral, a diagonal gives the two triangles a common side for free. Here BD is that side, and the given angles sit at its two ends, each beside a given side.

A and C lie on opposite sides of the diagonal BD, so the equal angles are alternate angles and AB ∥ CD as well. With AB = CD too, ABCD is a parallelogram, the shape Quant Q.18 of this shift defines.

Key facts

Congruence criteria: SSS, SAS, ASA, AAS, and RHS for right triangles.
In SAS, the angle must lie between the two given sides.
AAA and SSA do not prove congruence.
Once triangles are congruent, their remaining parts match (CPCT), so here AD = CB.

Study next

Choosing between ASA and AAS when two angles are givenRHS congruence in right trianglesUsing CPCT to prove sides or angles equal after a congruence

Common traps

Calling it SSS by counting AD = CB, which is a result of the congruence, not a given
Missing the common side BD, which the stem never states

12 Sep 2024, 09:00, Quant Q.17 tests the same included-angle condition: with AB = FD and ∠A = ∠D, SAS needs the other side at that angle, and the key is AC = DE.

10 Sep 2024, 09:00, Quant Q.3 asks which criterion cannot prove two triangles congruent, keyed angle-angle-angle.

Related PYQs

No directly related past PYQ was found.

Topic: Congruence and similarity of triangles — all 20 SSC CGL questions on it, every solved shift.