Question

if ad bisects <edi, then id=ed <ade=<ida ia=ae all of the above

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal parts. If \(AD\) bisects \(\angle EDI\), then \(\angle ADE=\angle IDA\).

Step2: Analyze \(ID = ED\)

There is no information given in the problem statement (only that \(AD\) bisects \(\angle EDI\)) to suggest that \(ID = ED\). For \(ID = ED\), we would need additional information like \(\triangle IDE\) being isosceles with \(ID = ED\) based on some other property (not just the angle - bisector).

Step3: Analyze \(IA = AE\)

Just because \(AD\) bisects \(\angle EDI\) does not mean \(IA = AE\). For \(IA = AE\), we would need \(AD\) to be a median (a line segment joining a vertex to the mid - point of the opposite side), which is not stated. The angle - bisector theorem relates the ratio of the adjacent sides to the ratio of the segments of the opposite side, but without knowing the ratio of \(ID\) to \(ED\), we cannot conclude \(IA = AE\).

Answer:

\(\angle ADE=\angle IDA\)