Given
![\Delta\text{ABC\textasciitilde}\Delta\text{DEF}]()
(triangle ABC similar to triangle DEF)
This means the corresponding sides are proportional.
The corresponding sides are:
AB corresponds to DE
AC corresponds to DF
BC corresponds to EF
All the angles are equal, as in
Angle A = Angle D
Angle B = Angle E
Angle C = Angle F
Now, looking at the statements,
A. BC = EF
This must not be true. They can be equal, but also proportional to each other.
This is not a must, hence this isn't correct.
B. AB/DE=AC/DF
Yes, this must be true. The corresponding sides (AB to DE and AC to DF ) are in fact proportional.
C. m∠C=m∠F
Angle C corresponds to Angle F and they must be equal.
Thus, this is correct.
D. m∠A/m∠D=m∠B/m∠E
Since Angle A and Angle D are equal, the ratio "m∠A/m∠D" must be 1.
Also, Angle B and Angle E are equal, the ratio "m∠B/m∠E" must be 1 as well.
Thus,
1 = 1
The ratio holds true and this statement is true.
Answer: B, C, and D