Question

in exercises 1 - 6, decide whether it is possible to prove that the triangles are congruent. if it is possible, state the theorem or postulate you would use. explain your reasoning. (lessons 4.3 and 4.4) 4.

Explanation:

Step1: Identify the common side

Both triangles share the side \(MK\). So, \(MK = MK\) (reflexive property).

Step2: Analyze the given angles

We are given that \(\angle JMK=\angle LKM\) and \(\angle JKM = \angle LMK\).

Step3: Apply the ASA (Angle - Side - Angle) congruence criterion

In \(\triangle JMK\) and \(\triangle LKM\), we have:

• \(\angle JMK=\angle LKM\) (given)
• \(MK = MK\) (common side)
• \(\angle JKM=\angle LMK\) (given)

By the ASA (Angle - Side - Angle) congruence postulate, \(\triangle JMK\cong\triangle LKM\)

Answer:

It is possible to prove the triangles are congruent. We use the ASA (Angle - Side - Angle) postulate.