In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB= 30 cm, find the perimeter of the quadrilateral ARPQ.

In a ΔABC, D, E and F are, respectively, the mid points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.

In a triangle ∠ABC, ∠A =50°, ∠B =60° and ∠C = 70°. Find the measure of the angles of the triangle formed by joining the mid-points of the sides of this triangle.

In a ΔABC, median AD is produced to X such that AD=DX. Prove that ABXC is a parallelogram.

In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects EF at Q. Prove that AQ=QP.