Which of the following is not a sufficient condition for two triangles to be congruent?

Analyze the question: You are asked which option is not enough to prove that two triangles are congruent (identical in shape and size).

Concept: Congruence conditions

Two triangles are congruent if any one of these holds:

• SSS: all three pairs of corresponding sides are equal.
• SAS: two pairs of sides and the included angle (the angle between them) are equal.
• ASA / AAS: two pairs of angles and one pair of corresponding sides are equal.
• RHS (for right-angled triangles): hypotenuse and one side are equal.

Check each option

• A. AAS: Two angles fix the third angle, so this is equivalent to ASA. Sufficient.
• B. SSS: Three sides fix the triangle completely. Sufficient.
• C. SAS: Two sides with the angle between them fix the triangle. Sufficient.
• D. SSA: Two sides and a non-included angle. This can produce two different triangles (the "ambiguous case"). For example, take side a = 5 cm, side b = 8 cm, and angle A = 30°. Side a can swing to meet the base at two different points, giving two non-congruent triangles. So SSA is not sufficient.

(The one exception is when the angle is a right angle, which is the RHS condition, but plain SSA does not guarantee congruence in general.)

**Answer: D.

Exam tip: Remember that "SSA" spells a rude word in reverse (ASS) and is the one that doesn't work. Another way: the angle must be between the two sides (SAS) or the matching side can be anywhere as long as you have two angles (AAS/ASA). SSA fails because the angle isn't between the sides.