For a parallelogram A B C D , if L and M are mid-points of B C and C D , then A L + A M =

Step-by-step solution

Given, A B C D is a parallelogram L, M are mid points of sides B C, C D respectively B L= 1 2 B C D M= 1 2 D C In A B C , array r A B + B L = A L A B + 1 2 B C = A L array In A D M , aligned & A D + D M = A M & A D + 1 2 D C = A M aligned Eqs. (i) + (ii) aligned A L + A M & = A B + 1 2 B C + A D + 1 2 D C & = A B + 1 2 B C + B C + 1 2 A B & = 3 2 A B + 3 2 B C & .= 3 2 ( A B + B C = B C )= 3 2 A C = A B ] aligned Hence, option (2) is correct.