Question

are these scalene triangles similar?
(image of two triangles with vertices t, u, v and s, with segments labeled 72, 52, 48, 86 intersecting at w)
options: yes, no

Explanation:

Step1: Identify vertical angles

Angles at \( W \) are vertical angles, so \( \angle TWU \cong \angle SWV \).

Step2: Check side ratios

For similarity (by SAS similarity), the ratios of corresponding sides should be equal. Calculate \( \frac{TW}{SW}=\frac{72}{48}=\frac{3}{2} \) and \( \frac{UW}{VW}=\frac{52}{86}=\frac{26}{43} \).

Step3: Compare ratios

Since \( \frac{3}{2}
eq\frac{26}{43} \), the sides around the equal angles are not proportional. Thus, the triangles are not similar.

Answer:

no