Discussion
In \(\triangle ABC\), if the median AD is perpendicular to the side BC, then the triangle is:
Answer: C
A median from a vertex to the opposite side divides the opposite side into two equal parts (BD = DC). If this median is also perpendicular to the side, it acts as an altitude.
In \(\triangle ADB\) and \(\triangle ADC\), we have BD = DC, AD is common, and \(\angle ADB = \angle ADC = 90°\). By the SAS (Side-Angle-Side) congruence rule, \(\triangle ADB \cong \triangle ADC\).
Therefore, the corresponding sides AB and AC must be equal. A triangle with two equal sides is an isosceles triangle.
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