The proof for AL + AM = 3/2 AC is given below.
Given that ABCD is a parallelogram, we know that opposite sides are equal and parallel. Therefore, AB = CD and BC = AD.
Since L and M are the midpoints of BC and CD respectively, we can express AL and AM in terms of AB and AD:
AL = (1/2)AC + CL
AM = (1/2)AC - CM
Substituting BC = AD into the expression for CL, we get:
CL = (1/2)BC = (1/2)AD
Substituting CL and CM into the expressions for AL and AM, we get:
AL = (1/2)AC + (1/2)AD
AM = (1/2)AC - (1/2)AD
Adding AL and AM, we get:
AL + AM = (1/2)AC + (1/2)AD + (1/2)AC - (1/2)AD
AL + AM = 2(1/2)AC
AL + AM = 3/2 AC
Therefore, AL + AM = 3/2 AC.