Final answer:
Triangles similar to triangle ABC must have the same angles: 86 degrees, 47 degrees, and 47 degrees. The lengths of the sides are irrelevant for similarity as long as the angles are congruent, under the AA similarity postulate.
Step-by-step explanation:
We're determining which triangles are similar to triangle ABC, where angle A is 86 degrees and angle B is 47 degrees. Triangles are similar if they have the same angle measurements, meaning they are congruent refers to angles, but their sides can be different lengths, scaled in proportion to each other. Since the sum of angles in a triangle is always 180 degrees, we can find that angle C in triangle ABC is 180 - 86 - 47 = 47 degrees.
For another triangle to be similar to ABC, it would need to have angles of 86 degrees, 47 degrees, and 47 degrees. The actual length of the sides does not affect similarity as long as the angles remain consistent. If a triangle has these angles, no matter the side lengths, it is similar to triangle ABC under the rules of AA (Angle-Angle) similarity postulate, which states that two triangles are similar if they have two congruent angles, with the third angle inevitably being congruent as well due to the 180-degree sum rule.