The figure below shows segments AC and EF which intersect at point B. Segment AF is parallel to segment EC.

Which of these facts is used to prove that triangle ABF is similar to triangle CBE?
Select one:
a. Angle AFB is congruent to angle CBE.
b. Angle ABF is congruent to angle CBE.
c. Line segment BC is congruent to line segment BE.
d. Line segment AB is congruent to line segment FB.

Question

The figure below shows segments AC and EF which intersect at point B. Segment AF is parallel to segment EC.

Which of these facts is used to prove that triangle ABF is similar to triangle CBE?
Select one:
a. Angle AFB is congruent to angle CBE.
b. Angle ABF is congruent to angle CBE.
c. Line segment BC is congruent to line segment BE.
d. Line segment AB is congruent to line segment FB.

simplymarie_x · Answer

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mathstudent55 · Answer

This is the situation you have.
I numbered the angles to be able to explain more easily.
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mathstudent55 · Answer

Since the two marked lines are parallel, angles 3 and 4 are congruent because of alternate interior angles. Angles 5 and 6 are also congruent because of alternate interior angles.
Angles 1 and 2 are congruent because of vertical angles.
You only need two pairs of congruent angles to prove triangles similar.

mathstudent55 · Answer

Choice A. states that angles 3 and 2 are congruent.
Do you know that they are?

mathstudent55 · Answer

We only know these three pairs of angles to be congruent.
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