Q. 6 Solve the following questions: (Any one)(1) Prove that three times the sum of the squares of the side of atriangle is equal to four times the sum of squares of the medians ofthat triangle.(2) In AABC, seg MN I side BC. A-M-B and A-N-C. Seg MNBMABdivides A ABC into two parts equal in area. Determine

Q. 6 Solve the following questions: (Any one)(1) Prove that three time

1.	Q. 6 Solve the following questions: (Any one)(1) Prove that three times the sum of the squares of the side of atriangle is equal to four times the sum of squares of the medians ofthat triangle.(2) In AABC, seg MN I side BC. A-M-B and A-N-C. Seg MNBMABdivides A ABC into two parts equal in area. Determine
Answer» theorem states that the sum of the squares of two sides of a triangle is equal to twice the square of the median on the third side plus half the square of the third side.Hence AB2+ AC2= 2BD2+2AD2=2×(½BC)2+2AD2 = ½ BC2+ 2AD2∴ 2AB2+ 2AC2= BC2+ 4AD2 → (1)Similarly, we get2AB2+ 2BC2= AC2+ 4BE2→ (2)2BC2+ 2AC2= AB2+ 4CF2→ (3)Adding (1) (2) and (3), we get4AB2+ 4BC2+ 4AC2= AB2+ BC2+ AC2+ 4AD2+ 4BE2+ 4CF23(AB2+ BC2+ AC2) = 4(AD2+ BE2+ CF2) Hence, three times the sum of squares of the sides of a triangle is equal to four times the sum of squares of the medians of the triangle.