Question

determine if triangle $nop$ and triangle $qrs$ 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 $\boldsymbol{checkmark}$ similar.

Explanation:

Step1: Match sides to angle

First, identify the sides adjacent to the given angle in $\triangle QRS$: $QR=24$, $QS=33$. In $\triangle NOP$, the sides are $OP=8$, $NO=9$, $NP=11$.

Step2: Calculate side ratios

Compute ratios of corresponding sides:
$\frac{QR}{OP}=\frac{24}{8}=3$
$\frac{QS}{NO}=\frac{33}{9}=\frac{11}{3}\approx3.67$
$\frac{RS}{NP}=\frac{24}{11}\approx2.18$

Step3: Check similarity conditions

For SAS similarity, two sides must be in proportion and the included angle equal. Here, the included angle in $\triangle NOP$ is unknown, and the side ratios are not equal. For SSS similarity, all three side ratios must be equal, which they are not.

Answer:

The triangles are not similar.