+44 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$ [asy] unitsize(1 cm); pair P, Q, R; P = (1,3); Q = (0,0); R = (4,0); draw(P--Q--R--cycle); label("$P$", P, N); label("$Q$", Q, SW); label("$R$", R, SE); label("$5$", (P + Q)/2, NW, red);mehr .. +44 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$ [asy] unitsize(1 cm); pair P, Q, R; P = (1,3); Q = (0,0); R = (4,0); draw(P--Q--R--cycle); label("$P$", P, N); label("$Q$", Q, SW); label("$R$", R, SE); label("$5$", (P + Q)/2, NW, red);mehr .. +44 +44 +44 Find the area of the triangle. [asy] unitsize(1 cm); pair A, B, C; A = (1,2); B = (0,0); C = (4,0); draw(A--B--C--cycle); label("$\frac{4}{3}$", (A + B)/2, NW, red); label("$2$", (A + C)/2, NE, red); label("$\frac{8}{3}$", (B + C)/2, S, red); [/asy]
mehr .. +44 +44 In the diagram below, $\angle PQR = \angle PRQ = \angle STR = \angle TSR$, $RQ = 8$, and $SQ = 3$. Find $PQ$. [asy] unitsize(5 cm); pair A,B,C,D,E; A = (0, 0.9); B = (-0.4, 0); C = (0.4, 0); D = (-0.275, 0.16); E = (0.11, 0.65); draw(A--B); draw(A--C);mehr .. +44 +44 +44
