Question

PLEASE HELP

Under what conditions would triangle DEF be similar to triangle ABC? Drag and drop the choices to make the statement correct.

Answer 1

Explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.