Question

1. a) aas not congruent b) sss d) asa

Explanation:

Step1: Analyze triangle congruence criteria

We have two triangles with two sides marked as equal (from the tick marks) and a pair of vertical angles? Wait, no, let's check the angles. Wait, the given: two sides are equal (marked with ticks), and the included angle? Wait, no, let's see the criteria. AAS: two angles and a non - included side. SSS: three sides. ASA: two angles and included side. But wait, in the diagram, we have two sides equal (the tick - marked sides) and a pair of angles (the angles at the intersection, vertical angles? Wait, no, maybe the angles at the vertices. Wait, actually, if we look at the triangles, we have two sides equal (marked) and a pair of angles (the angles at the non - included side? Wait, no, let's re - evaluate. Wait, the problem is about triangle congruence. Let's recall the criteria:

• AAS: If two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent.
• SSS: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
• ASA: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

But in the given diagram, we have two sides marked as equal (so two sides), and what about the angles? Wait, maybe the triangles have two sides equal and a non - included angle? Wait, no, SSA is not a congruence criterion. Wait, maybe the correct answer is AAS? Wait, no, let's look again. Wait, the two triangles: let's assume that we have two sides equal (marked) and a pair of angles (the angles at the vertices). Wait, maybe the triangles satisfy AAS? Wait, no, maybe I made a mistake. Wait, the options are AAS, SSS, Not congruent, ASA. Wait, let's check the number of congruent parts. We have two sides equal (from the tick marks) and one angle? Wait, no, maybe the vertical angles are equal. Wait, if we have two sides and a non - included angle, that's SSA, which is not a valid congruence criterion (except for right triangles, but these are not right triangles). Wait, but maybe the diagram has two angles and a side. Wait, no, the key here is that with the given markings (two sides equal and a pair of angles), but if the sides are not the included sides for the angles, then SSA is not valid. Wait, but maybe the triangles are not congruent? Wait, no, wait the options: A) AAS, B) SSS, C) Not congruent, D) ASA. Wait, let's re - examine. If we have two sides equal (marked) and a pair of angles (say, the angles at the vertices), but if the angle is not included between the two sides, then SSA doesn't work. So the triangles are not congruent? Wait, no, maybe I'm wrong. Wait, let's think again. The two triangles: we have two sides with ticks (so two sides equal), and a pair of angles (maybe vertical angles). But vertical angles are equal, but if the sides are not the included sides, then SSA is not a congruence condition. So the triangles are not congruent. So the correct option is C (Not congruent). Wait, but let's check the options. The option C is "Not congruent".

Step2: Match with the options

Among the options A (AAS), B (SSS), C (Not congruent), D (ASA), the triangles do not satisfy AAS (we don't have two angles and a non - included side), SSS (we only have two sides marked as equal, not three), ASA (we don't have two angles and included side). So the triangles are not congruent.

Answer:

C. Not congruent