Question

here is a conjecture. two triangles must be congruent if they have these pairs of corresponding congruent parts: two sides one angle not between the two sides when is this conjecture true? always sometimes never

Explanation:

Step1: Recall congruence criteria

The congruence criteria for triangles are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg) for right - angled triangles. The given condition is two sides and a non - included angle.

Step2: Consider counter - examples

For non - right - angled triangles, the SSA (Side - Side - Angle) condition does not guarantee congruence. For example, we can construct two non - congruent triangles with two sides of equal length and a non - included angle of equal measure. But for right - angled triangles (where one of the sides is the hypotenuse and the other is a leg), the HL (which is a special case of SSA) criterion works.

Answer:

Sometimes