Question

in the figure, ( in = ck ) and ( overline{ik} parallel overline{nc} ). what congruence statement proves ( \triangle kni cong \triangle nkc )?

Explanation:

Step1: Analyze the given information

We know \(IN = CK\) and \(\overline{IK}\parallel\overline{NC}\). When \(\overline{IK}\parallel\overline{NC}\), then \(\angle NIK=\angle CKN\) (alternate - interior angles). Also, \(NK = KN\) (common side).

Step2: Apply the congruence criterion

We have two sides and the included angle. For \(\triangle KNI\) and \(\triangle NKC\), \(IN = CK\) (given), \(\angle NIK=\angle CKN\) (from parallel lines), and \(NK = KN\) (common side). The \(SAS\) (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

B. SAS