# Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

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stuth1

In the given rectangle LMNO, it is given that MN=4 and ON=10.
In the rectangle RSTU, UT=3 and ST=8.
Rectangles LMNO and RSTU are similar if $$\displaystyle{\frac{{{O}{N}}}{{{S}{T}}}}={\frac{{{M}{N}}}{{{U}{T}}}}$$
Now,
$$\displaystyle{\frac{{{O}{N}}}{{{S}{T}}}}={\frac{{{10}}}{{{8}}}}$$
$$\displaystyle={\frac{{{5}}}{{{4}}}}$$
$$\displaystyle{\frac{{{M}{N}}}{{{U}{T}}}}={\frac{{{4}}}{{{3}}}}$$
$$\displaystyle{\frac{{{O}{N}}}{{{S}{T}}}}\ne{\frac{{{M}{N}}}{{{U}{T}}}}$$
So, rectangles LMNO and RSTU are not similar