Question

which statements about the figure to the right are true? which of the following statements are correct? select all that apply. a. \\( \overline { m j } \cong \overline { n l } \\) b. \\( \overline { k n } \cong \overline { k l } \\) c. \\( \triangle k m j \cong \triangle k n l \\) d. \\( \angle k j n \cong \angle k l m \\)

Explanation:

Step1: Analyze option A

Since \(JN = ML\) (given from the figure's markings) and \(NM\) is common. So \(JN+NM=ML + NM\), which means \(MJ=NL\). By the definition of congruent segments (\(MJ\cong NL\)), option A is correct.

Step2: Analyze option B

There is no information in the figure to suggest that \(KN = KL\). Just because there are some segment - equal markings in the figure does not imply \(KN\cong KL\). So option B is incorrect.

Step3: Analyze option C

We know \(MJ = NL\) (from step 1), \(KM=KN\) (given from the figure's markings), and \(\angle KJM=\angle KLM\) (if we assume some base - angle relationships in the larger triangle \(JKL\)). By the Side - Angle - Side (SAS) congruence criterion (\(\triangle KMJ\) and \(\triangle KNL\): \(MJ = NL\), \(KM = KN\), \(\angle KJM=\angle KLM\)), \(\triangle KMJ\cong\triangle KNL\). So option C is correct.

Step4: Analyze option D

Since \(JK = LK\) (assuming from the symmetry of the figure where \(KN = KM\) and \(JN=ML\) and using the properties of isosceles triangles in \(\triangle JKL\)), \(\angle KJN=\angle KLM\) (base angles of an isosceles triangle \(\triangle JKL\)). So option D is correct.

Answer:

A. \( \overline{MJ}\cong\overline{NL}\), C. \( \triangle KMJ\cong\triangle KNL\), D. \( \angle KJN\cong\angle KLM\)