Question

determine if triangle $ghi$ and triangle $jkl$ are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer
attempt are
are not
the triangles $\boldsymbol{sim}$ similar.

Explanation:

Step1: Match sides around given angle

First, identify the sides adjacent to the known angle in each triangle. For $\triangle GHI$, the sides are $GH=27$, $GI=37$. For $\triangle JKL$, the sides adjacent to $\angle L=48^\circ$ are $LK=40$, $LJ=70$. We check the ratios of corresponding sides:
$\frac{GH}{LK} = \frac{27}{40} = 0.675$, $\frac{GI}{LJ} = \frac{37}{70} \approx 0.529$

Step2: Compare side ratios

Since $\frac{27}{40}
eq \frac{37}{70}$, the ratios of the sides surrounding the potential included angle are not equal. There is no other given angle to test AA similarity, and SSS similarity also fails as all side ratios would not match.

Step3: Conclude similarity status

Because the conditions for triangle similarity (AA, SAS, SSS) are not satisfied, the triangles are not similar.

Answer:

The triangles are not similar.