Question

a. name the midsegments and sides that are parallel in (\triangle fhk).
b. name the midsegments that are half as long as each side of (\triangle fhk).
a. name the midsegments and sides that are parallel in (\triangle fhk). select all that apply.
□ a. (overline{fk}paralleloverline{gj})
□ b. (overline{hk}paralleloverline{jl})
□ c. (overline{fk}paralleloverline{gl})
□ d. (overline{hk}paralleloverline{gl})
□ e. (overline{fh}paralleloverline{gj})
□ f. (overline{fh}paralleloverline{jl})
□ g. there are no parallel segments.

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to the third side of the triangle.

Step2: Analyze each option

• For option A: \( \overline{FK}\) and \( \overline{GJ}\) are not parallel.
• For option B: \( \overline{HK}\) and \( \overline{JL}\) are parallel. Because \(JL\) is a mid - segment of \(\triangle FHK\) (by the mid - segment theorem, since \(J\) and \(L\) are mid - points of \(HK\) and \(FK\) respectively).
• For option C: \( \overline{FK}\) and \( \overline{GL}\) are not parallel.
• For option D: \( \overline{HK}\) and \( \overline{GL}\) are parallel. Because \(GL\) is a mid - segment of \(\triangle FHK\) (since \(G\) and \(L\) are mid - points of \(FH\) and \(FK\) respectively).
• For option E: \( \overline{FH}\) and \( \overline{GJ}\) are parallel. Because \(GJ\) is a mid - segment of \(\triangle FHK\) (since \(G\) and \(J\) are mid - points of \(FH\) and \(HK\) respectively).
• For option F: \( \overline{FH}\) and \( \overline{JL}\) are not parallel.
• For option G: This is incorrect as we have found parallel segments.

Answer:

B. \( \overline{HK}\parallel\overline{JL}\), D. \( \overline{HK}\parallel\overline{GL}\), E. \( \overline{FH}\parallel\overline{GJ}\)