For the points A,B,C,D is given that C belongs to AB, M belongs to AD and D doesn't belong to AB, prove that the plane (ABD) is the same as (CDM)

Question

For the points $A,B,C,D$ is given that $C$ belongs to $AB$, $M$ belongs to $AD$ and $D$ doesn't belong to $AB$, prove that the plane $(ABD)$ is the same as $(CDM)$. Here is drawing:

I tried to prove that $C$ and $D$ are lying on one line, but I failed, also I don't know how this would have helped me.

Answer 1

Let $\alpha$ the plane given by $ABD$. Then $C \in \alpha$ and $ M \in \alpha$ because these point are on lines of this plane. So, since $D \in \alpha$ and three point give one only plane, than $CMD$ are in the same plane $\alpha$.