This is homework.
I need to show that every AR is contractible.
All I can basically do here is list definitions:
A space $Y$ is AR if: $X$ is metrizable, $A$ is closed subset of $X$ and $f: A \mapsto Y$ is continuous, then $f$ has a continuous extension $g: X \mapsto Y$.
A space $Y$ is contractible if $id_Y :Y \mapsto Y$ is homotopic to a constant map.
I was thinking if I could use the fact that every AR is path connected and also every contractible space is path connected.