Question

which shows two triangles that are congruent by asa?

Explanation:

Step1: Recall ASA Congruence

ASA (Angle - Side - Angle) congruence criterion states that 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.

Step2: Analyze Each Option

• First Option (Top - two triangles with arc marks): The two triangles have two angles marked as equal (the arc - marked angles) and the included side (the side between the two angles) is common in terms of the way the triangles are drawn (since they are congruent in shape with the same angle markings and the included side length would be the same as they are identical in appearance with the same angle - side - angle configuration). So this seems to fit ASA.
• Second Option (Two triangles with tick marks): The markings here seem to be about sides and a non - included angle, more like AAS or SSA which is not ASA.
• Third Option (Two triangles with a common vertex): The markings here are about a side and an angle, but not the correct angle - side - angle included side configuration for ASA.
• Fourth Option (Right - triangle with a perpendicular): This seems to be about a right - triangle and a median or altitude, not the ASA configuration.

Answer:

The top - most figure (the first one with two triangles having arc - marked angles and a common - looking included side)