SOLUTION
The polygons are enclosed together to form a triangle.
To know if the triangle are similar, we use the ratio of the sides,
Using the Sides-Sides-Sides(SSS) rule which states that two triangles are similar if all the corresponding three sides of the given triangles are in the same proportion.
From triangle EFG, we have
[tex]\begin{gathered} |EF|=8\text{ units } \\ |FG|=4\text{unit} \\ |EG|=8\text{units } \end{gathered}[/tex]
Considering the triangle JLR, we have
[tex]\begin{gathered} |JL|=4\text{unit} \\ |LR|=2\text{unit } \\ |JR|=4\text{unit} \end{gathered}[/tex]
Comparing the ratio of the sides,
we have
[tex]\begin{gathered} \frac{|EF|}{|JL|}=\frac{8}{4}=2 \\ \text{Also} \\ \frac{|FG|}{|LR|}=\frac{4}{2}=2 \\ \text{And} \\ \frac{|EG|}{|JR|}=\frac{8}{4}=2 \end{gathered}[/tex]
Since the sides are in the same proportion,
Hence
The polygons are similar
