Question

problem 4
here is parallelogram abcd:
prove segment am is congruent to segment cm.
type your response in the space below.

Explanation:

Step1: Use the property of parallelogram

In parallelogram \(ABCD\), \(AB\parallel CD\) and \(AB = CD\).

Step2: Prove \(\triangle ABM\cong\triangle CDM\)

Since \(AB\parallel CD\), \(\angle ABM=\angle CDM\) (alternate - interior angles) and \(\angle BAM=\angle DCM\) (alternate - interior angles). Also, \(AB = CD\). By the Angle - Angle - Side (AAS) congruence criterion, \(\triangle ABM\cong\triangle CDM\).

Step3: Use the property of congruent triangles

If \(\triangle ABM\cong\triangle CDM\), then the corresponding parts are congruent. So, \(AM = CM\) (corresponding sides of congruent triangles).

Answer:

Since in parallelogram \(ABCD\), \(\triangle ABM\cong\triangle CDM\) (by AAS, as \(AB = CD\), \(\angle ABM=\angle CDM\), \(\angle BAM=\angle DCM\)), then \(AM = CM\) (corresponding sides of congruent triangles). So segment \(AM\) is congruent to segment \(CM\).