Question

Let ABCD be a parallelogram, with M the midpoint of DA, and diagonal AC of length 36. Let G be the intersection of MB and AC and draw in diagonal DB. What is the length of AG?

Answer 1

try to prove triangle AGM is similar to triangle CGM

Answer 2

once you do, you see the smaller triangle's sides are exactly 1/2 the bigger triangle's sides

using x= AG, the length of the corresponding side GC is 2x
together the segments add to 36
we find 3x=36 and x=12