Question

1. in the diagram below, ( kf ) is the perpendicular bisector of ( gh ). complete the statement: ( angle kgf cong angle )____?

a. ( angle fkg )
b. ( angle kf )
c. ( angle khf )
d. ( angle kfh )

Explanation:

Step1: Recall the property of perpendicular bisector

Since \(KF\) is the perpendicular bisector of \(GH\), we know that \(KG = KH\) (any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment). Also, \(GF=FH\) (definition of bisector) and \(KF = KF\) (common side).

Step2: Use SSS (Side - Side - Side) congruence criterion

By SSS congruence, \(\triangle KGF\cong\triangle KHF\).

Step3: Use corresponding parts of congruent triangles

If \(\triangle KGF\cong\triangle KHF\), then \(\angle KGF\cong\angle KHF\) (corresponding parts of congruent triangles are congruent).

Answer:

C. \(\angle KHF\)