Question

question
determine if triangle qrs and triangle tuv are or are not similar, and, if they are, state how you know.
(note that figures are not necessarily drawn to scale)
answer
attempt 1 out of 1
the triangles
similar.
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Explanation:

Step1: Calculate missing angle in $\triangle QRS$

The sum of angles in a triangle is $180^\circ$. For $\triangle QRS$:
$\angle S = 180^\circ - 41^\circ - 76^\circ = 63^\circ$

Step2: Compare side ratios

Check ratios of corresponding sides around the $41^\circ$ angle:
$\frac{QR}{TU} = \frac{8}{16} = \frac{1}{2}$, $\frac{QS}{TV} = \frac{9}{18} = \frac{1}{2}$

Step3: Verify SAS similarity

The included angle ($41^\circ$) is equal, and the surrounding sides are proportional.

Answer:

The triangles are similar, by the Side-Angle-Side (SAS) Similarity Criterion.