Question

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

Explanation:

Step1: Identify given congruent parts

In $\triangle JKL$, $\angle J = 58^\circ$. In $\triangle MNO$, $\angle M = 58^\circ$, so $\angle J \cong \angle M$. Also, $\overline{MO} \cong \overline{MN}$ (marked congruent sides).

Step2: Check similarity criteria

For similarity, we need either AA (two congruent angles), SSS (proportional sides), or SAS (proportional sides with included congruent angle). In $\triangle JKL$, we only know one angle, and no side relationships to $\triangle MNO$. The congruent sides in $\triangle MNO$ do not give us a proportional pair with sides of $\triangle JKL$.

Step3: Evaluate information sufficiency

We lack enough data to confirm proportional sides or a second pair of congruent angles to satisfy any similarity postulate.

Answer:

There is not enough information to determine whether the triangles are similar.