Question

select the correct answer. given: fg || kl how could you show fh/lj = if/il in the figure? use aa to show triangle fih is similar to triangle lji. use aa to show triangle fih is similar to triangle lji. use sas to show triangle fih is similar to triangle lji. use sas to show triangle fih is similar to triangle lji.

Explanation:

Step1: Identify corresponding angles

Since $\overline{FG}\parallel\overline{KL}$, corresponding - angles are equal. In $\triangle FI H$ and $\triangle LIJ$, $\angle F=\angle L$ (corresponding angles for parallel lines $\overline{FG}$ and $\overline{KL}$) and $\angle I$ is common to both triangles.

Step2: Apply AA similarity criterion

By the AA (angle - angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the two triangles are similar. So, $\triangle FIH\sim\triangle LIJ$.

Answer:

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