Question

in the diagram below, $\angle nom \cong \angle klm$. if $km = 20$, $nm = 16$, $kl = 15$, and $ml = 22.5$, find the length of $\overline{mo}$. figures are not necessarily drawn to scale.

Explanation:

Step1: Identify similar triangles

$\triangle NOM \sim \triangle KLM$ (by AA similarity, since $\angle NOM \cong \angle KLM$ and $\angle OMN \cong \angle LMK$ as vertical angles)

Step2: Set up proportion

Corresponding sides are proportional: $\frac{MO}{ML} = \frac{NM}{KM}$

Step3: Substitute known values

$\frac{MO}{22.5} = \frac{16}{20}$

Step4: Solve for $MO$

$MO = 22.5 \times \frac{16}{20}$
$MO = 22.5 \times 0.8$

Answer:

18