Solve the following problems : Given: S, T, and U are the midpoints of RP , PQ , and QR respectively. Prove: △SPT≅△UTQ.

Answer:Hence Proved △ SPT ≅ △ UTQStep-by-step explanation:Given: S, T, and U are the midpoints of Segment RP , segment PQ , and segment QR respectively of Δ PQR.To prove: △ SPT ≅ △ UTQProof:∵ T is is the midpoint of PQ.Hence PT = PQ    ⇒equation 1Now,Midpoint theorem is given below;The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.By, Midpoint theorem;TS║QRAlso, [tex]TS = \frac{1}{2} QR[/tex]Hence, TS = QU (U is the midpoint QR) ⇒ equation 2Also by Midpoint theorem;TU║PRAlso, [tex]TU = \frac{1}{2} PR[/tex]Hence, TU = PS (S is the midpoint QR) ⇒ equation 3Now in △SPT and △UTQ.PT = PQ (from equation 1)TS = QU (from equation 2)PS = TU (from equation 3)By S.S.S Congruence Property,△ SPT ≅ △ UTQ ...... Hence Proved