determine if triangle jkl and triangle mno are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Question

Accepted Answer

# Explanation:
## Step1: Find the third angle of triangle $JKL$
The sum of angles in a triangle is $180^{\circ}$. Let the third angle of $\triangle JKL$ be $\angle J$. Then $\angle J=180^{\circ}-(72^{\circ} + 45^{\circ})$.
$$
\begin{align*}
\angle J&=180^{\circ}-117^{\circ}\
\angle J& = 63^{\circ}
\end{align*}
$$
## Step2: Find the third angle of triangle $MNO$
Let the third angle of $\triangle MNO$ be $\angle M$. Then $\angle M=180^{\circ}-(45^{\circ}+72^{\circ})$
$$
\begin{align*}
\angle M&=180^{\circ}-117^{\circ}\
\angle M&=63^{\circ}
\end{align*}
$$
## Step3: Check for similarity using AA (Angle - Angle) criterion
In $\triangle JKL$ and $\triangle MNO$, $\angle K=\angle N = 45^{\circ}$, $\angle L=\angle O=72^{\circ}$ and $\angle J=\angle M = 63^{\circ}$. By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar), $\triangle JKL\sim\triangle MNO$

# Answer:
Triangles $JKL$ and $MNO$ are similar. By the AA (Angle - Angle) similarity criterion, since $\angle K=\angle N$, $\angle L=\angle O$ (and $\angle J=\angle M$),  $\triangle JKL\sim\triangle MNO$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the third angle of triangle \(JKL\)

Step2: Find the third angle of triangle \(MNO\)

Step3: Check for similarity using AA (Angle - Angle) criterion

Answer: