If two figures are similar, all of their pairs of corresponding sides have the same ratio:
To prove if the given figures are similar find the ratio between corresponding sides (to identify corresponding sides start with the smaller side in both figures and follow this logic):
[tex]\begin{gathered} \frac{AB}{YZ}=\frac{40}{25}=1.6 \\ \\ \frac{AC}{YX}=\frac{50}{31.25}=1.6 \\ \\ \frac{BC}{ZX}=\frac{60}{37.5}=1.6 \end{gathered}[/tex]
As the ratio between corresponding sides is the same (1.6); triangle ABC is similar to traingle YZX
Transformations from ABC to YZX: ABC (preimage) is dilated to get YZX (Image)
Find the factor of dilation:
[tex]\begin{gathered} Fd=\frac{Image}{Preimage} \\ \\ Fd=\frac{YZ}{AB}=\frac{25}{40}=\frac{5}{8} \end{gathered}[/tex]
Then, the transformation from ABC to YZX is a dilation with a factor of 5/8
