Question

given: in triangle abc, ∠b ≅ ∠c
prove: \overline{ab} ≅ \overline{ac}

complete the paragraph proof.
we are given that ∠b ≅ ∠c. assume segment ab is not congruent to segment ac.
if ab > ac, then m∠c > m∠b by the converse of the triangle parts relationship theorem. if ab < ac, then m∠c < m∠b by the converse of the triangle parts relationship theorem.
but by the definition of congruent, we know the measure of angle b equals the measure of dropdown by the given statement. therefore, we conclusion: ab = ac, and \overline{ab} ≅ \overline{ac}.
dropdown options: angle a, angle c, segment ac

Explanation:

We are given that $\angle B \cong \angle C$. By the definition of congruent angles, their measures are equal, so $m\angle B = m\angle C$. The dropdown is asking for the angle whose measure is equal to $\angle B$'s measure, and from the given $\angle B \cong \angle C$, it should be $\angle C$.

Answer:

angle C