Question
Given ΔABC ~ ΔDEF, which must be true? Select all that apply.
A. BC = EF
B. ABDE=ACDF
C. m∠C=m∠F
D. m∠Am∠D=m∠Bm∠E
A. BC = EF
B. ABDE=ACDF
C. m∠C=m∠F
D. m∠Am∠D=m∠Bm∠E
Answers
GPT-4o mini
Given that triangles ΔABC and ΔDEF are similar (ΔABC ~ ΔDEF), we know that the corresponding sides are in proportion, and the corresponding angles are equal. Let's analyze the options provided:
A. **BC = EF**
This statement is not necessarily true because while the lengths of the sides are proportional (e.g., BC/EF = k for some constant k), they are not necessarily equal unless the triangles are congruent, which is not implied by similarity alone.
B. **ABDE = ACDF**
This statement seems to be a typographical error as it does not clearly represent any valid geometric relationship. It appears to be a misrepresentation of a relationship involving areas or segments. Without clarification, we cannot determine the truthiness.
C. **m∠C = m∠F**
This statement is true. Since the triangles are similar, their corresponding angles are equal. So, angle C in triangle ABC corresponds to angle F in triangle DEF.
D. **m∠A * m∠D = m∠B * m∠E**
This statement is not true in general. The product of angles is not a property that holds for similar triangles.
Therefore, the only correct statement is:
C. m∠C = m∠F
In summary, the true statements are:
- C. m∠C = m∠F
A. **BC = EF**
This statement is not necessarily true because while the lengths of the sides are proportional (e.g., BC/EF = k for some constant k), they are not necessarily equal unless the triangles are congruent, which is not implied by similarity alone.
B. **ABDE = ACDF**
This statement seems to be a typographical error as it does not clearly represent any valid geometric relationship. It appears to be a misrepresentation of a relationship involving areas or segments. Without clarification, we cannot determine the truthiness.
C. **m∠C = m∠F**
This statement is true. Since the triangles are similar, their corresponding angles are equal. So, angle C in triangle ABC corresponds to angle F in triangle DEF.
D. **m∠A * m∠D = m∠B * m∠E**
This statement is not true in general. The product of angles is not a property that holds for similar triangles.
Therefore, the only correct statement is:
C. m∠C = m∠F
In summary, the true statements are:
- C. m∠C = m∠F