Question

1. What must be true in order for triangles DEF and ABC to be similar? Be very specific about the
properties of the angles and sides of these two triangles.
с
F
A
B
D
E

Answer 1

Answer/Step-by-step explanation:

For ∆ABC and ∆DEF to be similar the following must be true:

1. ∠A ≅ ∠D

2. ∠B ≅ ∠E

3. ∠C ≅ ∠F

4. The ratio of the length of their corresponding sides must be equal and proportional.

That is:

$\frac{\overline{AB}}{\overline{DE}} = \frac{\overline{BC}}{\overline{EF}} = \frac{\overline{AC}}{\overline{DF}}$

If all these are true, then ∆ABC ~ ∆DEF, because the corresponding angles of two similar shapes are equal, while the ratio of their corresponding side lengths are equal.