notice, the angle at the vertex N, is shared by both triangles, so is the same angle in the small one as well as on the large one.
now, notice the sides proportions,
[tex]\bf \cfrac{HN}{MN}=\cfrac{GN}{LN}\implies \cfrac{32}{10+32}=\cfrac{40}{12.5+40}\implies \cfrac{32}{42}=\cfrac{40}{52\frac{1}{2}}
\\\\\\
\cfrac{16}{21}=\cfrac{\frac{40}{1}}{\frac{105}{2}}
\implies
\cfrac{16}{21}=\cfrac{40}{1}\cdot \cfrac{2}{105}\implies \cfrac{16}{21}=\cfrac{8}{1}\cdot \cfrac{2}{21}\implies \cfrac{16}{21}=\cfrac{16}{21}[/tex]
they're the same proportion.
then the trianlgles are similar by SAS, two sides and an angle between them.
