Question

consider the two triangles shown below.
note: the triangles are not drawn to scale.
are the two triangles congruent?
choose 1 answer:
a yes
b no
c there is not enough information to say.

Explanation:

Step1: Identify congruence criteria

We use triangle congruence criteria (e.g., ASA, SAS, SSS). Here, both triangles have a right angle (implied by the right angle symbol), one pair of equal sides (the double - marked sides), one pair of equal sides (the single - marked sides), and the included angle (the acute angle) is equal. Wait, actually, let's re - examine. The two triangles: one side is equal (single mark), one side is equal (double mark), and the included angle (the angle between the side with single mark and the side with double mark? No, wait, the right angle and the acute angle. Wait, actually, looking at the triangles, they are right - angled triangles? Wait, no, the right angle is at the bottom right? Wait, the triangles have a right angle (the square corner), one side with single tick, one side with double tick, and the acute angle at the left is equal. Wait, let's use the SAS (Side - Angle - Side) congruence criterion. The two triangles: we have two sides and the included angle? Wait, no, the angle between the side with single tick and the side with double tick? Wait, no, the right angle and the acute angle. Wait, actually, in the two triangles, we have: one side (double tick) equal, one side (single tick) equal, and the included angle (the angle between the side with single tick and the side with the right angle? Wait, no, the angle at the left (the acute angle) is equal, the side with single tick is equal, and the side with double tick is equal. Wait, actually, let's think again. The triangles: both have a right angle (so the right angles are equal), one side with single tick (so those sides are equal), one side with double tick (so those sides are equal). Wait, but in triangle congruence, for SAS, it's two sides and the included angle. Wait, maybe it's ASA? Wait, no, let's see: the two triangles have: angle (the acute angle) equal, side (single tick) equal, and the right angle equal? No, that would be AAS. Wait, AAS (Angle - Angle - Side) or SAS. Wait, actually, looking at the diagram, the two triangles: one side (double tick) is equal, one side (single tick) is equal, and the included angle (the angle between the side with single tick and the side with double tick? No, the angle at the left (acute angle) is equal, the side with single tick is adjacent to the acute angle and the right angle. Wait, maybe it's SAS. Let's confirm: in triangle congruence, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent (SAS). Here, the two sides with ticks (single and double) and the included angle (the angle between them, which is the right angle? Wait, no, the right angle is at the bottom right. Wait, the acute angle at the left, the side with single tick, and the side with double tick: the angle between the side with single tick and the side with double tick is the right angle? Wait, no, the right angle is between the base and the double - ticked side. Wait, maybe I'm overcomplicating. The key is that the two triangles have two sides equal (single tick and double tick) and the included angle equal (the angle between the single - ticked side and the double - ticked side? Or the angle at the left). Wait, actually, the two triangles: we can see that they have two sides equal (the single - ticked sides and the double - ticked sides) and the included angle (the angle between the single - ticked side and the double - ticked side? No, the angle at the left is equal, the single - ticked side is equal, and the double - ticked side is equal. Wait, maybe it's SAS. So by SAS congruence criterion, the two triangles are congruent.

Step2: Conclusion

Since the two triangles satisfy the SAS (or AAS) congruence criterion (two sides and the included angle, or two angles and a non - included side), the two triangles are congruent.

Answer:

A. Yes