Question

are the triangles congruent? if so, by what theorem? yes by aaa yes by sss yes by hl not congruent

Explanation:

Step1: Recall congruence theorems

Triangles can be congruent by SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - angled triangles). AAA (Angle - Angle - Angle) only shows similarity, not congruence.

Step2: Analyze the given triangles

The markings on the triangles show that two sides and the included angle (but here we can also think in terms of SSS if we consider the side - side - side correspondence from the markings). Wait, actually, if we assume the sides are marked as equal (two sides with one mark and another side with two marks), then by SSS (if all three corresponding sides are equal as per the markings), the triangles are congruent.

Answer:

Yes by SSS