Question

The triangles below are similar.

mr024-1.jpg

Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle C B A is similar to triangle F E D
Triangle C B A is similar to triangle F D E
Triangle B A C is similar to triangle E F D
Triangle B A C is similar to triangle E D F
Triangle A B C is similar to triangle D E F
Triangle A B C is similar to triangle D F E

Answer 1

To determine the correct similarity statements, we need to understand that if two triangles are similar, their corresponding angles are equal, and the sides are in proportion. The similarity notation typically uses the order of the vertices to show which angles correspond to each other.

Given the triangles CBA and FED, let's analyze the statements you provided:

1. Triangle CBA is similar to triangle FED
2. Triangle CBA is similar to triangle FDE
3. Triangle BAC is similar to triangle EFD
4. Triangle BAC is similar to triangle EDF
5. Triangle ABC is similar to triangle DEF
6. Triangle ABC is similar to triangle DFE

To check for similarity, we make sure that the corresponding angles match in the correct order. Without a visual representation or specific angle measures, we can only affirm the corresponding angles based on the labels provided:

Assuming:
- Triangle CBA has angles at vertices C, B, and A respectively
- Triangle FED has angles at vertices F, E, and D respectively

If C corresponds to F, B to E, and A to D, then the similarity statement would be written as:
- CBA ~ FED

Using that correspondence, you can check the other statements:

- CBA ~ FDE (This is not correct because F corresponds to C, E to B, and D to A)
- BAC ~ EFD (This is not correct based on our angle correspondence)
- BAC ~ EDF (This is not correct based on our angle correspondence)
- ABC ~ DEF (This should be correct if A corresponds to D, B to E, and C to F)
- ABC ~ DFE (This is not correct based on our angle correspondence)

**Correct similarity statements from the collection based on presumed correspondence would be:**
- Triangle CBA is similar to triangle FED
- Triangle ABC is similar to triangle DEF

If the correspondence changes, you would need to adjust the similarity statements accordingly.