Determine whether the two triangles are similar \triangle TSU\sim \triangle

Clifland 2021-08-11 Answered
Determine whether the two triangles are similar. If they are, complete the similarity statement.
Select all that apply.
\(\displaystyle\triangle{T}{S}{U}\sim\triangle\) ?
image
The triangles are not similar.
\(\displaystyle\triangle{T}{S}{U}\sim\triangle{W}{V}{U}\)
\(\displaystyle\triangle{T}{S}{U}\sim\triangle{V}{W}{U}\)
By SAS similarity
By SSS similarity
By AA similarity

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Expert Answer

Szeteib
Answered 2021-08-12 Author has 5271 answers

Observe that
\(\displaystyle{T}{S} \parallel {V}{W}\) (parallel)
In \(\displaystyle\triangle{T}{S}{U}\ {\quad\text{and}\quad}\ \triangle{W}{V}{U}\)
\(\displaystyle\angle{S}{T}{U}=\angle{V}{W}{U}\) (Interior Alternate Angle)
Also \(\displaystyle{T}{S}{U}=\angle{U}{V}{W}\) (Interior Alternate Angle)
So, \(\displaystyle\triangle{T}{S}{U}\sim\triangle{W}{V}{U}\) by AA Similarity
Also \(\displaystyle\triangle{W}{V}{U}\) in same \(\displaystyle\triangle{V}{W}{U}\)
Hence Correct options are
\(\displaystyle\triangle{T}{S}{U}\sim\triangle{W}{V}{U}\)
\(\displaystyle\triangle{T}{S}{U}\sim\triangle{V}{W}{U}\)
By AA similarity

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