Question

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

Explanation:

Using the Triangle Midsegment Theorem: a midsegment of a triangle is parallel to the opposite side, and its length is half the length of the opposite side.

1. For side $\overline{FH}$ (length 5+5=10), the midsegment opposite is $\overline{JL}$, so $\overline{FH} \parallel \overline{JL}$.
2. For side $\overline{HK}$ (length 6+6=12), the midsegment opposite is $\overline{GL}$, so $\overline{HK} \parallel \overline{GL}$.
3. For side $\overline{FK}$ (length 7+7=14), the midsegment opposite is $\overline{GJ}$, so $\overline{FK} \parallel \overline{GJ}$.

Answer:

A. $\overline{FK}\parallel\overline{GJ}$
C. $\overline{FH}\parallel\overline{JL}$
F. $\overline{HK}\parallel\overline{GL}$