Question

Triangles ABC and DEF are shown in the figure. In triangle ABC, angle A measures 34 degrees and side AB measures 8 inches. In triangle DEF, angle F measures 56 degr EF measures 8 inches. Which of the following statements best describes the relationship between triangles ABC and DEF?

Answer 1

Triangles ABC and DEF are not similar.

For two triangles to be similar, their corresponding angles must be congruent, and their corresponding sides must be proportional.

In triangle ABC, angle A measures 34 degrees, but in triangle DEF, angle F measures 56 degrees. These angles are not congruent, so the triangles do not have the same shape.

Additionally, side AB measures 8 inches in triangle ABC, and side EF measures 8 inches in triangle DEF. While these sides have the same length, it does not necessarily mean that the triangles are similar. Similar triangles would have proportional sides, meaning that all corresponding sides would be in the same ratio. Since the angles are not congruent, we cannot conclude that the triangles are similar.