Question

copy the triangle and highlight congruent parts. mark and highlight additional congruent parts that can be proved congru on your paper. select what additional information is required order to know that the triangles are congruent by sas. ∠lmn ≅ ∠jmn ∠lnm ≅ ∠jnm ∠lmn ≅ ∠jnm ln ≅ nj

Explanation:

Step1: Recall SAS Congruence Rule

The SAS (Side - Angle - Side) congruence rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the Given Triangles

In \(\triangle LMN\) and \(\triangle JMN\), we know that \(LM = JM\) (given as congruent sides in the figure) and \(MN=MN\) (common side). For SAS, we need the included angles. The included angle for side \(LM\) and \(MN\) in \(\triangle LMN\) is \(\angle LMN\), and the included angle for side \(JM\) and \(MN\) in \(\triangle JMN\) is \(\angle JMN\).

Step3: Check the Options

• For \(\angle LNM\cong\angle JNM\), these angles are not the included angles for the sides \(LM = JM\) and \(MN = MN\).
• For \(\angle LMN\cong\angle JNM\), these are not the correct included angles.
• For \(\overline{LN}\cong\overline{NJ}\), these are sides, but not the included sides for the SAS rule with the given equal sides \(LM = JM\) and \(MN=MN\).
• For \(\angle LMN\cong\angle JMN\), since \(LM = JM\), \(MN = MN\) (common side), and if \(\angle LMN\cong\angle JMN\) (the included angles), then by the SAS congruence rule \(\triangle LMN\cong\triangle JMN\)

Answer:

\(\angle LMN\cong\angle JMN\)