Data Sufficiency

I think my prep book may have an error in it. One of the data sufficiency questions has a triangle with an line drawn down. The question ask whether or not the two angles created by the line which looks like a bisector are equal. The second choice states that the two legs are equal to one another. If the two legs are equal that would mean that the triangle is an isosceles triangle. My question is with an isosceles triangle is it possible for a line drawn from the base to the vertex angle opposite the base to be anything other than an angle bisector?

osirus0830 wrote:My question is with an isosceles triangle is it possible for a line drawn from the base to the vertex angle opposite the base to be anything other than an angle bisector?

It is not possible as long as that line is perpendicular to the base. We know that the corresponding angles to the congruent sides are congruent, and they sum to 180 so they must each be 90 degrees. Therefore the line is perpendicular, and hence it bisects the angle.

raleigh wrote:

osirus0830 wrote:My question is with an isosceles triangle is it possible for a line drawn from the base to the vertex angle opposite the base to be anything other than an angle bisector?

It is not possible as long as that line is perpendicular to the base. We know that the corresponding angles to the congruent sides are congruent, and they sum to 180 so they must each be 90 degrees. Therefore the line is perpendicular, and hence it bisects the angle.

Thank you very much. Yeah choice one stated that the line was perpendicular, I guess I can't assume that the figure is drawn to scale. Thanks so much, I really appreciate the help.