Similar triangles — corresponding altitude / median / angle-bisector ratios = similarity ratio

Dependencies: AA similarity, SAS / SSS similarity (SSS and SAS similarity tests).

Statement

Let $\triangle ABC \sim \triangle A'B'C'$ with similarity ratio $k$, i.e.

Let $h$, $m$, $t$ denote, respectively, the altitude, median, and Angle bisector ⇔ equidistant from sides length from vertex $A$ in $\triangle ABC$ (each with foot on side $BC$); and $h'$, $m'$, $t'$ the corresponding cevians of the same kind in $\triangle A'B'C'$. Then

That is, every interior segment defined by similar triangles in a "corresponding" manner scales by the similarity ratio $k$.