Question

question
determine if triangle uww and triangle xyz are or are not similar, and, if they are, state how you know.
(note that figures are not necessarily drawn to scale.)
the triangles
similar.
answer attempt 1 out of 2
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Explanation:

Step1: Find missing angle in △UVW

First, calculate the third angle of △UVW. The sum of angles in a triangle is $180^\circ$.
$\angle U = 180^\circ - 61^\circ - 52^\circ = 67^\circ$

Step2: Compare side ratios

Check if corresponding sides are proportional. Match sides adjacent to the $52^\circ$ angle:
$\frac{UV}{XY} = \frac{10}{40} = \frac{1}{4}$, $\frac{VW}{YZ} = \frac{11}{44} = \frac{1}{4}$

Step3: Verify SAS similarity

We have a pair of equal included angles ($\angle V = \angle Y = 52^\circ$) and the surrounding sides are in equal proportion. This satisfies the Side-Angle-Side (SAS) similarity criterion.

Answer:

The triangles are similar, by the SAS similarity criterion (the included $52^\circ$ angles are equal, and the adjacent side pairs are proportional with a ratio of $\frac{1}{4}$).