Question

1. uy = 27 yd; wx = 45 yd; vw = 50 yd; uv = 36 yd vy = ________ ; vx = ________

Explanation:

Step1: Check for similar triangles

Since $\angle U = \angle X$ and $\angle YVU=\angle WVX$ (vertically - opposite angles), $\triangle YUV\sim\triangle XVW$ by the AA (angle - angle) similarity criterion.

Step2: Set up the proportion for similar - triangles

For similar triangles $\triangle YUV$ and $\triangle XVW$, we have the proportion $\frac{UY}{WX}=\frac{UV}{VX}=\frac{VY}{VW}$.
We know that $\frac{UY}{WX}=\frac{27}{45}=\frac{3}{5}$, and $\frac{UV}{VX}=\frac{3}{5}$, $\frac{VY}{VW}=\frac{3}{5}$.

Step3: Find VX

Given $UV = 36$ yd, from $\frac{UV}{VX}=\frac{3}{5}$, we can cross - multiply: $3VX=5\times36$. Then $VX=\frac{5\times36}{3}=60$ yd.

Step4: Find VY

Given $VW = 50$ yd, from $\frac{VY}{VW}=\frac{3}{5}$, we cross - multiply: $5VY = 3\times50$. Then $VY=\frac{3\times50}{5}=30$ yd.

Answer:

$VY = 30$ yd; $VX = 60$ yd