Question

In the figure, O is the point inside triangleABC, and P,Q and R are the mid-points of OA, OB and OC respectively. Prove that trianglePQR ~ triangleABC.

Answer 1

I 

The line AB is parallel to PQ, BC || QR, AC || PR because triangles AOC and POR are similar, and same applies to the two other pairs of triangles having O as a common apex. This makes the internal triangle PQR similar to ABC, because of corresponding angles between parallel lines. The sides of PQR are each half the length of the “parent” ABC, because the vertices of PQR are midpoints of the sides of ABC.