Question

select the correct answer. given: fg || kl how could you show (\frac{fh}{fj}=\frac{if}{il}) in the figure? use aa to show triangle fih is similar to triangle lij. use sas to show triangle fih is similar to triangle lij. use aa to show triangle fih is similar to triangle lji. use sas to show triangle fih is similar to triangle lji.

Explanation:

Step1: Analyze parallel - line properties

Since $\overline{FG}\parallel\overline{KL}$, corresponding angles are equal. In $\triangle FIH$ and $\triangle LIJ$, $\angle FIH=\angle LIJ$ (vertically - opposite angles) and $\angle IFH=\angle ILJ$ (corresponding angles due to $\overline{FG}\parallel\overline{KL}$).

Step2: Apply similarity criterion

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the two triangles are similar. Here, since two pairs of angles are equal, $\triangle FIH\sim\triangle LIJ$ by AA similarity.

Answer:

Use AA to show triangle FIH is similar to triangle LIJ.