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.
a. $overline{fh}||overline{gj}$
b. $overline{fk}||overline{gj}$
c. $overline{hk}||overline{jl}$
d. $overline{hk}||overline{gl}$
e. $overline{fh}||overline{jl}$
f. $overline{fk}||overline{gl}$
g. there are no parallel segments.

Explanation:

Step1: Recall midsegment theorem

A midsegment of a triangle is parallel to a side of the triangle, and connects the midpoints of the other two sides.

Step2: Match midsegments to parallel sides

• $\overline{GJ}$ connects midpoints of $\overline{FH}$ and $\overline{HK}$, so it is parallel to $\overline{FK}$.
• $\overline{JL}$ connects midpoints of $\overline{HK}$ and $\overline{FK}$, so it is parallel to $\overline{FH}$.
• $\overline{GL}$ connects midpoints of $\overline{FH}$ and $\overline{FK}$, so it is parallel to $\overline{HK}$.

Step3: Match to given options

• $\overline{FH} \parallel \overline{JL}$ (Option E), $\overline{FK} \parallel \overline{GJ}$ (Option B), $\overline{HK} \parallel \overline{GL}$ (Option D) are the correct parallel pairs.

Answer:

B. $\overline{FK}\parallel\overline{GJ}$, D. $\overline{HK}\parallel\overline{GL}$, E. $\overline{FH}\parallel\overline{JL}$