Question

are these scalene triangles similar? yes no

Explanation:

Step1: Calculate the ratio of corresponding sides

We have two sides of the first triangle \(VUW\) as \(42\) and \(36\), and two sides of the second triangle \(GHI\) as \(63\) and \(54\).
The ratio of \(42\) to \(63\) is \(\frac{42}{63}=\frac{2}{3}\) (divide numerator and denominator by \(21\)).
The ratio of \(36\) to \(54\) is \(\frac{36}{54}=\frac{2}{3}\) (divide numerator and denominator by \(18\)).

Step2: Check the included - angle condition

The included angles (the marked angles) between the pairs of corresponding sides are equal.
By the Side - Angle - Side (SAS) similarity criterion, if the ratios of two pairs of corresponding sides are equal and the included angles are equal, then the triangles are similar.

Answer:

yes