Question

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

Answer 1

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