Work Step by Step
When the two midpoints (of the original triangle) are joined, we have created a mid-segment. A mid-segment is parallel to the 'base' of the original triangle. Corresponding angles on parallel lines are congruent. Therefore both angles formed by the mid-segment will be congruent to the corresponding angles of the original triangle. Since we have proven that two sets of corresponding angles (of the triangles) are congruent, the two triangles are congruent by AA.