Sure, I'd be happy to explain this to you!
Step 1: Understand that congruent triangles are identical - meaning their corresponding angles and sides must be equal.
Step 2: Identify correspondences. In congruent triangles ABC and DEF, the vertices are correspondingly named, meaning that vertex A corresponds to vertex D, B to E, and C to F.
Now, let's take each provided statement and see if it matches our understanding of congruent triangles.
Statement 1: m∠F=m∠B. In our correspondence of vertices, B corresponds to E, not F. So for congruent triangles, the measure of angle B should be equal to the measure of angle E, not F. Therefore, this statement is not true.
Statement 2: AC=DE. Sides AC in triangle ABC should correspond to DF in triangle DEF because vertex A corresponds to D and C corresponds to F. So it's not true to say that AC is equal to DE.
Statement 3: CB = DE. If you check our line of correspondence, side CB in triangle ABC corresponds exactly to side DE in triangle DEF (C corresponds to D and B corresponds to E). Therefore, the sides are equal and this statement is true.
Statement 4: m∠C=m∠F. Checking the corresponding vertices, angle C in triangle ABC corresponds to angle F in triangle DEF. Therefore, these angles are equal and this statement is true.
So, in conclusion, the statements "CB = DE" and "m∠C=m∠F" must be true about these triangles because of their congruence.