Question

Triangle DEF is similar to triangle ABC. What is the measure, in degrees, of angle F? Explain how you know.

A) 30 degrees
B) 45 degrees
C) 60 degrees
D) 90 degrees

Answer 1

The measure of angle F in triangle DEF is equal to the measure of angle B in triangle ABC.

Step-by-step explanation:

In similar triangles, corresponding angles are congruent. This means that if triangle DEF is similar to triangle ABC, their corresponding angles are equal. Angle F in triangle DEF corresponds to angle B in triangle ABC because angles are named in correspondence with their respective vertices. Therefore, if triangle DEF is similar to triangle ABC, angle F must have the same measure as angle B.

The concept of similar triangles involves proportional sides and congruent angles. If two triangles are similar, their corresponding angles are equal, and the ratios of their corresponding sides are equivalent. This fundamental principle enables us to determine that angle F in triangle DEF has the same measure as angle B in triangle ABC because of their correspondence within similar triangles. Therefore, the measure of angle F in triangle DEF is equivalent to the measure of angle B in triangle ABC due to their similarity. Hence, the correct answer is the angle B's measure from the options provided, which is not explicitly given in the question.