Question

question 6 of 40
is $\triangle abc$ similar to $\triangle def$? why or why not?

a. yes, because if at least one pair of angles are equal, the triangles are similar.
b. yes, because the angles are congruent and the sides are proportional.
c. we cannot tell because the third side is not given.
d. no, because although the angles are congruent, the sides are not.

Explanation:

Step1: Verify angle congruence

First, confirm all corresponding angles are equal:

• In $\triangle ABC$: $\angle A=25^\circ$, $\angle C=60^\circ$, $\angle B=180^\circ-25^\circ-60^\circ=95^\circ$
• In $\triangle DEF$: $\angle D=25^\circ$, $\angle F=60^\circ$, $\angle E=180^\circ-25^\circ-60^\circ=95^\circ$

All corresponding angles are congruent.

Step2: Check side proportionality

Calculate the ratio of corresponding sides:

• $\frac{AB}{DE}=\frac{8}{6}=\frac{4}{3}$
• $\frac{AC}{DF}=\frac{10}{7.5}=\frac{4}{3}$

The sides are proportional.

Step3: Evaluate options

Option A is incorrect (needs 2 congruent angles, not 1). Option C is incorrect (we can confirm similarity). Option D is incorrect (sides are proportional). Option B matches our findings.

Answer:

B. Yes, because the angles are congruent and the sides are proportional.