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

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

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Calculation:
Consider two triangles WXV and ZXY as shown as in the textbook.
$\mathrm{\angle }WXV\stackrel{\sim }{=}\mathrm{\angle }ZXY$
They are vertically opposite angles
Compare the corresponding sides, $\frac{WX}{ZX}=\frac{10}{15}=\frac{2}{3}$
Compare the corresponding sides, $\frac{VX}{YX}=\frac{12}{18}=\frac{2}{3}$
Thus,
$\frac{WX}{ZX}=\frac{VX}{YX}$
$\frac{2}{3}=\frac{2}{3}$
According to the SAS similarity theorem:
Therefore,
$\mathrm{△}WXV\sim \mathrm{△}ZXY$
Hence, $\mathrm{△}WXV\sim \mathrm{△}ZXY$ are similar with each other by the SAS similarity theorem