Question

points s, u, and t are the midpoints of the sides of △ pqr. which statements are correct? check all that apply. □ \\(\frac{1}{2}qp = ut\\) □ \\(\frac{1}{2}ts = rq\\) □ \\(su = pr\\) □ \\(\overline{su} \parallel \overline{rp}\\) □ \\(\overline{ut} \perp \overline{rp}\\)

Explanation:

Step1: Apply Midsegment Theorem

Midsegment = ½ opposite side, parallel to it.

Step2: Check each statement

1. $\frac{1}{2}QP = UT$: UT is midsegment for QP → Correct.
2. $\frac{1}{2}TS = RQ$: TS is midsegment for RQ → $\frac{1}{2}RQ=TS$ → Wrong.
3. $SU = PR$: SU is midsegment → $SU=\frac{1}{2}PR$ → Wrong.
4. $\overline{SU} \parallel \overline{RP}$: SU is midsegment for RP → Correct.
5. $\overline{UT} \perp \overline{RP}$: No right angle shown → Wrong.

Answer:

A. $\frac{1}{2}QP = UT$, D. $\overline{SU} \parallel \overline{RP}$