Groupoid Theory I, Higson's notes

Question

This is Example 7.22, page 100.

We first consider $G=TM$ a smooth groupoid with base space $M$. The source and range maps are the same projection maps $s,r:TM \rightarrow M, X_m \mapsto m$. Now I quote what the author writes,

If $G=TM$ then a Haar system is a smoothly varying system of translation invariant measures on the vector spaces $T_mM$.

Then, (I have broken down the claim into two parts), the author writes

1. Since a translation invariant measure on $T_mM$ is the same as a point in $\wedge^n T^*_mM$
2. we see a smooth Haar system on $TM$ is determined by a smooth measure on $M$.

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Thoughts: I am already confused at 1. Let us suppose we are working with $\Bbb R^n$. Then how is a translation measure determined by a point in $\wedge^n(\Bbb R^n)^* \cong \Bbb R$?