Question

1. select all that apply: in an isosceles triangle, if ab = ac, where does the perpendicular bisector of bc intersect the triangle? midpoint of bc at vertex c at vertex b at vertex a

Explanation:

1. Midpoint of BC: By definition, a perpendicular bisector of a segment (here, \( BC \)) passes through its midpoint. So the perpendicular bisector of \( BC \) must intersect \( BC \) at its midpoint.
2. At vertex A: In an isosceles triangle with \( AB = AC \), the triangle is symmetric about the line that is the perpendicular bisector of \( BC \). This line also passes through vertex \( A \) (since \( AB = AC \), \( A \) lies on the perpendicular bisector of \( BC \)).
3. At vertex B/C: The perpendicular bisector of \( BC \) is perpendicular to \( BC \) and passes through its midpoint. Vertex \( B \) and \( C \) lie on \( BC \), but the perpendicular bisector is not at \( B \) or \( C \) (unless \( BC = 0 \), which is impossible for a triangle). So these are incorrect.

Answer:

• Midpoint of BC
• At vertex A