Question

k is the midpoint of (overline{ij}) and (overline{hk}perpoverline{ij}). complete the proof that (\triangle hikcong\triangle hjk).

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Step2: Identify the sides and angle for \(\triangle HIK\) and \(\triangle HJK\)

We have \(IK\cong JK\) (from the definition of mid - point, statement 4), \(\angle HKI\cong\angle HKJ\) (statement 3), and \(HK\cong HK\) (statement 5, reflexive property).

Answer:

\(\triangle HIK\cong\triangle HJK\) by the SAS (Side - Angle - Side) congruence criterion. So the statement for line 6 is \(\triangle HIK\cong\triangle HJK\) and the reason is "SAS (Side - Angle - Side) Congruence Criterion".