Question

the two triangles are
show your work here
congruent based on ssa congruent based on sas
congruent based on asa congruent based on hl
not necessarily congruent

Explanation:

Step1: Recall congruence criteria

The SSA (Side - Side - Angle) is not a valid congruence criterion in general. The ASA (Angle - Side - Angle) requires two angles and the included side. The HL (Hypotenuse - Leg) is for right - angled triangles. The SAS (Side - Angle - Side) requires two sides and the included angle.

Step2: Analyze the given triangles

In the given triangles, we have two sides (marked with ticks) and the included angle (the non - marked angle is not relevant for SAS). But wait, no, actually, SSA is not a valid criterion. Let's check again. Wait, no, in the first triangle, we have two sides (say \(a\) and \(b\)) and an angle. In the second triangle, the sides are in a different order. For SAS, the angle must be between the two sides. Here, the given information does not satisfy SAS (because the angle is not between the two sides in a consistent way for both triangles). And since SSA is not a valid congruence rule (except in some special cases like right - angled triangles, but these are not right - angled), we cannot say the triangles are congruent.

Answer:

Not necessarily congruent