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 $delta fhk$.
$square$ e. $overline{hk}||overline{jl}$
$square$ g. there are no parallel segments.
$square$ f. $overline{hk}||overline{gl}$
b. name the midsegments that are half as long as each side of $delta fhk$. select all that apply.
$square$ a. $hj=\frac{1}{2}hk$
$square$ b. $jl=\frac{1}{2}fh$
$square$ c. $fl=\frac{1}{2}fk$
$square$ d. $gl=\frac{1}{2}hk$
$square$ e. $gj=\frac{1}{2}fk$
$square$ f. there are no midsegments that are half as long as any

Explanation:

Step1: Identify midsegment pairs

A midsegment of a triangle is parallel to a side and half its length.

• $\overline{GJ} \parallel \overline{FK}$, $\overline{GJ} = \frac{1}{2}FK$
• $\overline{GL} \parallel \overline{HK}$, $\overline{GL} = \frac{1}{2}HK$
• $\overline{LJ} \parallel \overline{FH}$, $\overline{LJ} = \frac{1}{2}FH$

Step2: Verify parallel segments

Match parallel pairs to options: $\overline{HK} \parallel \overline{GL}$ is correct.

Step3: Verify half-length midsegments

Check which options fit the midsegment rule:

• $\overline{GL} = \frac{1}{2}HK$ (matches $\overline{GL} \parallel \overline{HK}$ rule)
• $\overline{JL} = \frac{1}{2}FH$ (matches $\overline{LJ} \parallel \overline{FH}$ rule)

Answer:

Part a:

F. $\overline{HK}\parallel\overline{GL}$

Part b:

B. $\overline{JL}=\frac{1}{2}FH$
D. $\overline{GL}=\frac{1}{2}HK$