Question

8
not ~
© gina wilson (all things algebra), 2014

Explanation:

Step1: Calculate side ratios

$\frac{QR}{TR} = \frac{52}{63} \approx 0.825$, $\frac{SR}{UR} = \frac{39}{84} = \frac{13}{28} \approx 0.464$

Step2: Compare the ratios

Check if $\frac{QR}{TR} = \frac{SR}{UR}$
$\frac{52}{63}
eq \frac{39}{84}$

Step3: Verify vertical angles

$\angle QRS = \angle TRU$ (vertical angles are equal)

Step4: Check similarity condition

For SAS similarity, sides around equal angles must be proportional. Since the side ratios are not equal, the triangles do not satisfy SAS similarity. No other similarity criteria (AA, SSS) are met here.

Answer:

The triangles $\triangle QRS$ and $\triangle TRU$ are not similar, which matches the given "NOT ~" label.