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{hk}paralleloverline{gl})
b. (overline{fh}paralleloverline{jl})
c. (overline{fh}paralleloverline{gj})
d. (overline{hk}paralleloverline{jl})
e. (overline{fk}paralleloverline{gl})
f. (overline{fk}paralleloverline{gj})
g. there are no parallel segments.

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to a side of the triangle and half its length.

Step2: Identify mid - segments

In \(\triangle FHK\), \(GJ\), \(GL\), and \(JL\) are mid - segments.

• For mid - segment \(GL\): By the mid - segment theorem, \(GL\parallel HK\) (since \(GL\) is a mid - segment connecting the mid - points of \(FH\) and \(FK\)).
• For mid - segment \(JL\): \(JL\parallel FH\) (since \(JL\) is a mid - segment connecting the mid - points of \(HK\) and \(FK\)).
• For mid - segment \(GJ\): \(GJ\parallel FK\) (since \(GJ\) is a mid - segment connecting the mid - points of \(FH\) and \(HK\)).

So, the correct options are A, B, and F.

Answer:

A. \(\overline{HK}\parallel\overline{GL}\), B. \(\overline{FH}\parallel\overline{JL}\), F. \(\overline{FK}\parallel\overline{GJ}\)