Question

2 in isosceles triangle dac, segment ad is congruent to ac. kiran knows that the base angles of an isosceles triangle are congruent. what additional information does kiran need to know in order to show that ab is a perpendicular bisector of segment cd?

Explanation:

To show \( AB \) is the perpendicular bisector of \( CD \), we need \( AB \) to bisect \( CD \) (i.e., \( DB = BC \)) and \( AB \perp CD \). In isosceles \( \triangle DAC \) (\( AD = AC \)), if \( B \) is the midpoint of \( CD \) (or \( AB \) is the median), by the Isosceles Triangle Theorem (median from the apex is also the altitude and angle bisector), \( AB \) would be perpendicular to \( CD \). So the key additional info is that \( B \) is the midpoint of \( CD \) (or \( DB = BC \), or \( AB \) is the median of \( \triangle DAC \) to \( CD \)).

Answer:

Kiran needs to know that point \( B \) is the midpoint of segment \( CD \) (or \( DB = BC \), or \( AB \) is the median of \( \triangle DAC \) with respect to side \( CD \)).