## Geometry: Common Core (15th Edition)

$\triangle PQR$ ~ $\triangle TVW$ by the Side-Side-Side (SSS) Similarity Theorem.
We are given the measures of all the sides in the two triangles. Let's see if the Side-Side-Side Similarity Theorem can be applied here. The SSS Similarity Theorem states that if three sides in one triangle are proportional to the three sides of another triangle, then the two triangles are similar. Let's set up the ratios of corresponding sides in $\triangle PQR$ and $\triangle TVW$: $\frac{PQ}{TV} = \frac{10}{15}$ Divide the numerator and denominator by their greatest common factor, $5$: $\frac{PQ}{TV} = \frac{2}{3}$ Let's look at $QR$ and $VW$: $\frac{QR}{TV} = \frac{10}{15}$ Divide the numerator and denominator by their greatest common factor, $5$: $\frac{QR}{TV} = \frac{2}{3}$ Let's look at $RP$ and $WT$: $\frac{RP}{WT} = \frac{8}{12}$ Divide the numerator and denominator by their greatest common factor, $4$: $\frac{RP}{WT} = \frac{2}{3}$ Since all corresponding sides have a scale factor of $2:3$, $\triangle PQR$ ~ $\triangle TVW$ by the Side-Side-Side (SSS) Similarity Theorem.