Question

a. name the midsegments and sides that are parallel in $\triangle abc$
b. name the midsegments that are half as long as each side of the $\triangle abc$
$square$ e. $overline{ac}||overline{df}$
$square$ g. there are no parallel segments.
$square$ u. $ac||de$
$square$ f. $overline{ab}||overline{ef}$
b. name the midsegments that are half as long as each side of the $\triangle abc$. select all that apply.
$square$ a. $fc=\frac{1}{2}bc$
$square$ b. $ef=\frac{1}{2}ab$
$square$ c. $df=\frac{1}{2}ac$
$square$ d. $ad=\frac{1}{2}ab$
$square$ e. $de=\frac{1}{2}bc$
$square$ f. there are no midsegments that are half as long as any side

Explanation:

Step1: Identify midsegment parallel pairs

By Triangle Midsegment Theorem:

• $\overline{DF} \parallel \overline{AC}$
• $\overline{EF} \parallel \overline{AB}$
• $\overline{DE} \parallel \overline{BC}$

Step2: Match midsegment length rules

By Triangle Midsegment Theorem, midsegments are $\frac{1}{2}$ the length of their parallel sides:

• $\overline{EF} = \frac{1}{2}\overline{AB}$
• $\overline{DF} = \frac{1}{2}\overline{AC}$
• $\overline{DE} = \frac{1}{2}\overline{BC}$

Answer:

Part a (parallel segments, select all that apply):

E. $\overline{AC}\parallel\overline{DF}$, F. $\overline{AB}\parallel\overline{EF}$, (additionally $\overline{BC}\parallel\overline{DE}$ as a valid pair)

Part b (midsegments half the side length, select all that apply):

B. $EF=\frac{1}{2}AB$, C. $DF=\frac{1}{2}AC$, E. $DE=\frac{1}{2}BC$