Question

given △abc with $overline{ab}congoverline{ac}$, which of the following statements is true? a. △abc is equilateral. b. $angle acongangle b$ c. △abc is acute. d. $angle bcongangle c$

Explanation:

Step1: Recall triangle - type definitions

An equilateral triangle has all three sides equal. Here only \(AB = AC\), so it's not equilateral.

Step2: Recall angle - side relationships

In a triangle, if two sides are equal (\(AB\cong AC\)), then the angles opposite those sides are equal. The angles opposite \(AB\) and \(AC\) are \(\angle C\) and \(\angle B\) respectively. So \(\angle B\cong\angle C\). We cannot say \(\angle A\cong\angle B\) without more information. Also, just knowing two equal sides does not tell us if the triangle is acute.

Answer:

D. \(\angle B\cong\angle C\)