Question

a. name the midsegments and sides that are parallel in $delta abc$.
b. name the midsegments that are half as long as each side of the $delta abc$.
$square$ bc||ef
$square$ 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 $delta abc$. 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

Explanation:

Step1: Identify midsegment parallel pairs

By Triangle Midsegment Theorem:

• $\overline{DF} \parallel \overline{AC}$ (D,F are midpoints of AB, BC)
• $\overline{EF} \parallel \overline{AB}$ (E,F are midpoints of AC, BC)
• $\overline{DE} \parallel \overline{BC}$ (D,E are midpoints of AB, AC)

Step2: Match length relationships

Midsegment = $\frac{1}{2}$ parallel side:

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

Answer:

Part a (parallel midsegments/sides):

E. $\overline{AC}\parallel\overline{DF}$, F. $\overline{AB}\parallel\overline{EF}$, and the additional pair $\overline{BC}\parallel\overline{DE}$

Part b (midsegments half the side length):

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