△jkl and △mno are shown below.\nwhich statement is true?\n△jkl is similar to △mno.\n△jkl is not similar to…

Explanation:

Step1: Identify Angle and Side Info

In $\triangle JKL$ and $\triangle MNO$, $\angle J \cong \angle M$ (marked equal angles). Also, $JK$ and $MN$ are marked with 2 ticks (equal), $KL$ and $NO$ are marked with 2 ticks (equal)? Wait, no—wait, $\triangle JKL$ has $JK = KL$ (1 tick each), so it's isosceles with $\angle J = \angle L$. $\triangle MNO$: $MN = NO$ (2 ticks each), so isosceles with $\angle M = \angle O$. But also, $\angle J = \angle M$ (marked). So by AA (Angle - Angle) similarity: if two angles of one triangle are equal to two angles of another, triangles are similar. Wait, $\angle J = \angle M$, and since $\triangle JKL$ is isosceles ($JK = KL$), $\angle J = \angle L$; $\triangle MNO$ is isosceles ($MN = NO$), $\angle M = \angle O$. So $\angle L = \angle O$. Thus, two angles equal: $\angle J = \angle M$ and $\angle L = \angle O$, so AA similarity holds. Alternatively, SAS: $\angle J = \angle M$, and sides around the angle: $\frac{JK}{MN} = \frac{KL}{NO}$ (since $JK = KL$? Wait no, $JK$ and $MN$: wait the markings—$\triangle JKL$: $JK$ and $KL$ have 1 tick (so $JK = KL$). $\triangle MNO$: $MN$ and $NO$ have 2 ticks (so $MN = NO$). Wait, maybe the ratio: but also, $\angle J = \angle M$. Wait, maybe I misread the ticks. Wait the diagram: $\triangle JKL$: $JK$ and $KL$ have 1 red tick (so $JK = KL$). $\triangle MNO$: $MN$ and $NO$ have 2 red ticks (so $MN = NO$). Also, $\angle J$ and $\angle M$ are marked equal. So in $\triangle JKL$, sides $JK = KL$, so it's isosceles with base $JL$. In $\triangle MNO$, sides $MN = NO$, so isosceles with base $MO$. Now, $\angle J = \angle M$ (given). So the sides adjacent to $\angle J$ are $JK$ and $JL$? Wait no, $\angle J$ is between $JK$ and $JL$. $\angle M$ is between $MN$ and $MO$. Wait, maybe the sides: $JK$ corresponds to $MN$, $JL$ corresponds to $MO$, and $KL$ corresponds to $NO$? Wait, maybe the correct approach: AA similarity. Since $\angle J = \angle M$, and since $\triangle JKL$ is isosceles ($JK = KL$), $\angle J = \angle L$; $\triangle MNO$ is isosceles ($MN = NO$), $\angle M = \angle O$. Thus, $\angle L = \angle O$. So two angles: $\angle J = \angle M$ and $\angle L = \angle O$, so AA similarity. Therefore, $\triangle JKL \sim \triangle MNO$.

Step2: Conclude Similarity

By AA (Angle - Angle) similarity criterion, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Here, $\angle J \cong \angle M$ and $\angle L \cong \angle O$ (since both triangles are isosceles with equal vertex angles, their base angles are equal), so $\triangle JKL$ is similar to $\triangle MNO$.

Answer:

$\triangle JKL$ is similar to $\triangle MNO$. (So the first option: $\boldsymbol{\triangle JKL}$ is similar to $\boldsymbol{\triangle MNO}$.)