Question

To prove:The two triangles are similar using postulate or theorem.

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asked 2021-01-19

To prove:The two triangles are similar using postulate or theorem.
Given information:
The system triangles:
image

Expert Answers (1)

2021-01-20
Calculation:
Consider two triangles WXV and ZXY as shown as in the textbook.
\(\displaystyle\angle{W}{X}{V}\stackrel{\sim}{=}\angle{Z}{X}{Y}\)
They are vertically opposite angles
Compare the corresponding sides, \(\displaystyle\frac{{{W}{X}}}{{{Z}{X}}}=\frac{{10}}{{15}}=\frac{{2}}{{3}}\)
Compare the corresponding sides, \(\displaystyle\frac{{{V}{X}}}{{{Y}{X}}}=\frac{{12}}{{18}}=\frac{{2}}{{3}}\)
Thus,
\(\displaystyle\frac{{{W}{X}}}{{{Z}{X}}}=\frac{{{V}{X}}}{{{Y}{X}}}\)
\(\displaystyle\frac{{2}}{{3}}=\frac{{2}}{{3}}\)
According to the SAS similarity theorem:
Therefore,
\(\displaystyle\triangle{W}{X}{V}\sim\triangle{Z}{X}{Y}\)
Hence, \(\displaystyle\triangle{W}{X}{V}\sim\triangle{Z}{X}{Y}\) are similar with each other by the SAS similarity theorem
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