Question

problem 8 (problema 8)
here is parallelogram abcd:
aquí está el paralelogramo abcd:
prove segment am is congruent to segment cm.
demuestra que el segmento am es congruente con el segmento cm.

Explanation:

Step1: Recall parallelogram properties

In parallelogram \(ABCD\), \(AB \parallel CD\) and \(AB = CD\); diagonals bisect each other.

Step2: Identify congruent triangles

\(\angle ABM = \angle CDM\) (alternate interior angles, \(AB \parallel CD\)), \(AB = CD\), \(\angle BAM = \angle DCM\) (alternate interior angles). Thus, \(\triangle ABM \cong \triangle CDM\) (ASA).

Step3: Conclude congruent segments

Corresponding parts of congruent triangles are congruent: \(AM = CM\). So \(AM \cong CM\).

Answer:

Segment \(AM \cong CM\)