Question

are these scalene triangles similar?
yes
no

Explanation:

Step1: Check the ratio of sides

For triangle \(DEF\) and \(UVT\), we have \(\frac{40}{41}
eq\frac{56}{44}\) (since \(\frac{40}{41}\approx0.976\) and \(\frac{56}{44}=\frac{14}{11}\approx1.273\)).

Step2: Recall the similarity criteria

For two triangles to be similar, either AA (angle - angle), SAS (side - angle - side) or SSS (side - side - side) similarity criteria must be met. Here, even though \(\angle E=\angle T = 89^{\circ}\), the sides adjacent to the equal angles do not have a proportional ratio. So, SAS similarity is not satisfied.

Answer:

no