Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.) answer attempt 1 out of 2 jk is a segment bisector. jk is an angle bisector. j is the vertex of two angles that are congruent to one another. k is the vertex of two angles that are congruent to one another. k is the vertex of a right angle. j is the midpoint of a segment in the diagram.

Explanation:

Step1: Analyze segment - bisector property

There is no indication in the diagram that \(JK\) divides any segment into two equal - length parts. So, \(JK\) is not a segment bisector.

Step2: Analyze angle - bisector property

There is no indication in the diagram that \(JK\) divides any angle into two equal - measure angles. So, \(JK\) is not an angle bisector.

Step3: Check congruent angles at vertex \(J\)

Since \(FJ = JI\) (marked with equal - length segments), \(\triangle FJI\) is isosceles. In an isosceles triangle \(\triangle FJI\), the base - angles \(\angle IFJ\) and \(\angle FIJ\) are congruent, and \(J\) is the vertex of these two congruent angles.

Step4: Check congruent angles at vertex \(K\)

There is no information in the diagram to suggest that \(K\) is the vertex of two congruent angles.

Step5: Check right - angle at vertex \(K\)

There is no right - angle symbol or any information to suggest that \(K\) is the vertex of a right - angle.

Step6: Check mid - point property of \(J\)

Since \(FJ = JI\), \(J\) is the mid - point of segment \(FI\).

Answer:

J is the vertex of two angles that are congruent to one another.
J is the midpoint of a segment in the diagram.