In △ABC and △XYZ, AB = XY, BC = YZ, and CA = ZX. By which congruence rule are the two triangles congruent?

Question

In △ABC and △XYZ, AB = XY, BC = YZ, and CA = ZX. By which congruence rule are the two triangles congruent?

1. A. SSS (Correct answer)
2. B. SAS
3. C. ASA
4. D. RHS

Correct Answer

Option A — SSS

Detailed Solution & Explanation

The correct answer is SSS.

Key Points

• All three sides of one triangle are given equal to the corresponding three sides of the other: AB = XY, BC = YZ, CA = ZX.
• Three pairs of equal sides with no angle information is the SSS (Side-Side-Side) criterion.

Additional Information

• The congruence criteria in full: SSS, SAS (two sides and the included angle), ASA (two angles and the included side), AAS (two angles and a non-included side) and RHS (right angle, hypotenuse and one side, for right triangles only).
• SSA is not a valid criterion — two sides and a non-included angle can produce two different triangles, the "ambiguous case".
• AAA establishes only similarity, not congruence, since the triangles may differ in size while sharing all three angles.
• In SAS the angle must lie between the two sides; that word "included" is what the question type most often tests.

प्रश्न (हिन्दी में)

△ABC और △XYZ में, AB = XY, BC = YZ, और CA = ZX। दोनों त्रिभुज किस सर्वांगसमता नियम से सर्वांगसम हैं?

1. A. SSS
2. B. SAS
3. C. ASA
4. D. RHS