Proof with area segments in a triangle

Question

I have to show that $A M_CS$ and $M_CBS$ have the same area $X$ and that concerning areas $X=Y=Z$ is true.

I'm really stuck here, I would appreciate any help or tip...! How can I start here?

Answer 1

Hint: If $M_C$ is the midpoint of $AB$, then $A M_CS$ and $M_CBS$ have equal bases and share the same height.

Can you proceed for the first part?

For the second part, a similar approach, except consider the triangles $CM_CB$ and $CM_CA$. Are these areas equal? Express each of the areas in terms of $X, Y$ and $Z$.

Can you finish up for the second part?