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Please, please help me!

Triangle ABC is congruent to triangle DEF . Which statement must be true about the triangles?


m∠F=m∠B

AC = DE

CB = DE

m∠C=m∠F

2 Answers

3 votes

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.

User Belykh
by
4.3k points
0 votes
Triangle ABC is congruent to triangle DEF

m<A = m<D
m<B = m<E
m<C = m<F

AB = DE
BC = EF
AC = DF

So answer:
m∠C=m∠F
User Anshul Bansal
by
5.2k points
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