Question

△axy is similar to △abc. 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: Recall similar - triangle property

For similar triangles $\triangle AXY$ and $\triangle ABC$, the ratios of corresponding sides are equal. That is, $\frac{AX}{AB}=\frac{XY}{BC}=\frac{AY}{AC}$.

Step2: Solve for $BC$

From $\frac{XY}{BC}=\frac{AX}{AB}$, we can cross - multiply to get $BC = XY\cdot\frac{AB}{AX}$.

Answer:

None of the given options ($BC = AC$, $BC = XY$, $BC = XY\cdot\frac{AX}{AB}$) are correct. The correct formula for $BC$ given the similarity of $\triangle AXY$ and $\triangle ABC$ is $BC=XY\cdot\frac{AB}{AX}$.