Question

△fgh and △jkl are shown below.
which statement is true?
△fgh is similar to △jkl.
△fgh is not similar to △jkl.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify triangle properties

$\triangle FGH$ is isosceles with $FG = FH$, so $\angle G = \angle H$. $\triangle JKL$ is isosceles with $JK = JL$, so $\angle K = \angle L$.

Step2: Apply SAS similarity rule

The included angle between the equal sides is $\angle F$ for $\triangle FGH$ and $\angle J$ for $\triangle JKL$. We know $\frac{FG}{JK} = \frac{FH}{JL}$ (ratio of corresponding equal sides), and if two pairs of corresponding sides are in proportion and their included angles are equal, triangles are similar. For isosceles triangles with proportional equal sides, the included angles must be equal to maintain the triangle shape, so $\angle F = \angle J$. By SAS similarity criterion, the triangles are similar.

Answer:

$\triangle FGH$ is similar to $\triangle JKL$.