In Fig. 14.96, M, N and P are mid points of AB, AC and BC respectively. If MN=3 cm, NP=3.5 cm and MP = 2.5 cm, calculate BC, AB and AC.

In a ΔABC, BM and CN are perpendiculars from B and C respectively on any line passing through A. If L is the mid-point of BC, prove that ML=NL.

In Fig. 14.95, triangle ABC is right-angled at B. Given that AB=9 cm, AC=15 cm and D, E are the mid-points of the sides AB and AC respectively, calculate

(i) The length of BC

(ii) The area of ΔADE.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of ΔABC.

In Fig. 14.97, BE⊥AC. AD is any line from A to BC intersecting BE in H, P, Q and R are respectively the mid points of AH, AB and BC. Prove that ∠PQR = 90°