Question

points s, u, and t are the midpoints of the sides of △ pqr. which statements are correct? check all that apply. 1/2 qp = ut 1/2 ts = rq su = pr su || rp ut ⊥ rp

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side and half its length.

Step2: Analyze each option

• For $\frac{1}{2}QP = UT$:

Since \(U\) and \(T\) are mid - points of \(RQ\) and \(PR\) respectively, by the mid - segment theorem, \(UT\parallel QP\) and \(UT=\frac{1}{2}QP\).

• For \(\frac{1}{2}TS = RQ\):

By the mid - segment theorem, \(TS\parallel RQ\) and \(TS = \frac{1}{2}RQ\), not \(\frac{1}{2}TS=RQ\).

• For \(SU = PR\):

By the mid - segment theorem, \(SU=\frac{1}{2}PR\), not \(SU = PR\).

• For \(\overline{SU}\parallel\overline{RP}\):

Since \(S\) and \(U\) are mid - points of \(PQ\) and \(RQ\) respectively, by the mid - segment theorem, \(\overline{SU}\parallel\overline{RP}\).

• For \(\overline{UT}\perp\overline{RP}\):

There is no information given to suggest that \(UT\) is perpendicular to \(RP\). The mid - segment theorem only gives a parallel relationship ( \(UT\parallel QP\) ) and a length relationship ( \(UT=\frac{1}{2}QP\) )

Answer:

\(\frac{1}{2}QP = UT\) and \(\overline{SU}\parallel\overline{RP}\)