The picture below is of a baseball diamond. If the distance between 1st and 2nd base is the same as the distance between 2nd base and third base, and the angles at 2nd base are congruent (see picture), Are the two triangles made congruent? If so, what theorem tells us that?
Without a picture, it is not possible to determine whether the two triangles are congruent or not. To determine whether the triangles are congruent, we would need more information about the lengths of the sides or the sizes of the angles.
However, if we assume that the triangles are isosceles triangles (with two sides of equal length), then we can say that the triangles are congruent. In this case, the theorem that tells us that the two triangles are congruent is the Isosceles Triangle Theorem. According to this theorem, if in a triangle two sides are congruent, then the angles opposite those sides are also congruent.