Question

28.
given: in this figure, $overline{ld}$ and $overline{on}$ bisect each other.
are the triangles congruent? if so, how?
yes/no

Explanation:

Step1: Analyze bisecting segments

Since \( \overline{LD} \) and \( \overline{ON} \) bisect each other, \( LU = UD \) and \( OU = UN \).

Step2: Identify vertical angles

\( \angle L U O \) and \( \angle D U N \) are vertical angles, so \( \angle L U O=\angle D U N \).

Step3: Apply SAS congruence

We have \( LU = UD \), \( \angle L U O=\angle D U N \), and \( OU = UN \). By the Side - Angle - Side (SAS) congruence criterion, \( \triangle L U O\cong\triangle D U N \).

Answer:

Yes, by SAS (Side - Angle - Side) congruence criterion.