This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify properties of parallelogram PQRS. Since PQRS is a parallelogram, its opposite sides are parallel and equal in length. Therefore, we have: • PS QR • PQ SR • PS = QR • PQ = SR Step 2: Use the definitions of midpoints T and U. T is the midpoint of PS, so PT = TS = (1)/(2) PS. U is the midpoint of QR, so QU = UR = (1)/(2) QR. Step 3: Establish relationships between PT and QU. From Step 1, we know PS = QR. From Step 2, PT = (1)/(2) PS and QU = (1)/(2) QR. Substituting PS = QR into the midpoint equations, we get PT = (1)/(2) QR and QU = (1)/(2) QR. Thus, PT = QU. Also, since PS QR (from Step 1) and T lies on PS while U lies on QR, it follows that PT QU. Step 4: Prove that quadrilateral PTUQ is a parallelogram. Consider quadrilateral PTUQ. We have shown that PT QU and PT = QU. A quadrilateral with one pair of opposite sides that are both parallel and equal in length is a parallelogram. Therefore, PTUQ is a parallelogram. Step 5: Conclude the parallelism of TU and SR. Since PTUQ is a parallelogram, its opposite sides are parallel. Thus, TU PQ. From Step 1, we know that PQ SR. Since TU PQ and PQ SR, by the transitive property of parallel lines, we can conclude that TU SR. TU SR What's next? Send 'em! 📸