Determine whether the polygons \triangle RMP\ and\ \triangle UWX are similar.

smileycellist2 2021-08-11 Answered
Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
\(\displaystyle\triangle{R}{M}{P}\ {\quad\text{and}\quad}\ \triangle{U}{W}{X}\)
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Expert Answer

funblogC
Answered 2021-08-12 Author has 4966 answers
In \(\displaystyle\triangle{R}{M}{P}\) & \(\displaystyle\triangle{U}{W}{X}\)
\(\displaystyle{\frac{{{R}{M}}}{{{W}{X}}}}={\frac{{{8}}}{{{12}}}}={\frac{{{2}}}{{{3}}}}\)
\(\displaystyle\Rightarrow{\frac{{{R}{M}}}{{{W}{X}}}}={\frac{{{2}}}{{{3}}}}\)
Now
\(\displaystyle{\frac{{{M}{P}}}{{{W}{U}}}}={\frac{{{10}}}{{{15}}}}={\frac{{{2}}}{{{3}}}}\)
\(\displaystyle\Rightarrow{\frac{{{R}{M}}}{{{W}{X}}}}={\frac{{{M}{P}}}{{{W}{U}}}}\Rightarrow\ {S}{i}{m}{i}{l}{a}{r}{i}{t}{y}\ {R}{a}{t}{i}{o}\ ={\frac{{{2}}}{{{3}}}}\)
\(\displaystyle\therefore{\frac{{{R}{M}}}{{{M}{P}}}}={\frac{{{W}{X}}}{{{W}{U}}}}\Rightarrow\triangle{R}{M}{P}\sim\triangle{X}{W}{U}\)
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