Question

Can you please help me determine whether the polygons with the given vertices are similar?

Answer 1

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

`\begin{gathered} |EF|=8\text{ units } \\ |FG|=4\text{unit} \\ |EG|=8\text{units } \end{gathered}`

Considering the triangle JLR, we have

`\begin{gathered} |JL|=4\text{unit} \\ |LR|=2\text{unit } \\ |JR|=4\text{unit} \end{gathered}`

Comparing the ratio of the sides,

we have

`\begin{gathered} (|EF|)/(|JL|)=(8)/(4)=2 \\ \text{Also} \\ (|FG|)/(|LR|)=(4)/(2)=2 \\ \text{And} \\ (|EG|)/(|JR|)=(8)/(4)=2 \end{gathered}`

Since the sides are in the same proportion,

Hence

The polygons are similar