Question

which of the following expressions could be used to determine the length of segment bc? bc = ac bc = xy bc = xy·\\(\frac{ax}{ab}\\) bc = xy·\\(\frac{ab}{ax}\\)

Explanation:

Step1: Identify similar - triangles

If $\triangle AXY$ and $\triangle ABC$ are similar (by AA - similarity criterion if $XY\parallel BC$), the ratios of their corresponding sides are equal.
The ratio of corresponding sides of similar triangles gives $\frac{XY}{BC}=\frac{AX}{AB}$.

Step2: Solve for $BC$

Cross - multiply the proportion $\frac{XY}{BC}=\frac{AX}{AB}$ to get $BC = XY\cdot\frac{AB}{AX}$.

Answer:

$BC = XY\cdot\frac{AB}{AX}$