Answer: The answer is either m∠B = m∠E or m∠C = m∠F.
Step-by-step explanation: We are given two triangles, ΔABC and ΔDEF with m∠A = m∠D. We are to find the other fact that will guarantee that the two triangles are similar.
We know that the two triangles are similar if all the three angles of one triangle are equal in measurement to the corresponding three angles of the second triangle.
Also, if two angles of one triangle are congruent to the two corresponding angles of the other triangle, then the third pair of angles must also be congruent.
Therefore, if we have m∠B = m∠E or m∠C = m∠F, then we can conclude that the two triangles are similar.