Question

are these scalene triangles similar?
write a similarity statement.

Explanation:

Step1: Calculate the ratio of corresponding sides

For the sides \( \frac{42}{63}=\frac{2}{3} \), \( \frac{36}{54}=\frac{2}{3} \)

Step2: Check the similarity condition

Since the included angles (the marked angles) are equal and the ratios of the corresponding sides are equal (\( \frac{2}{3} \)), by the Side - Angle - Side (SAS) similarity criterion, the triangles are similar.

For the similarity statement, we match the vertices. The sides \( VU = 42 \) corresponds to \( HG=63 \), \( UW = 36 \) corresponds to \( GI = 54 \), and the included angles \( \angle U\) and \( \angle G\) are equal. So \( \triangle VUW\sim\triangle HGI \)

Answer:

yes; \( \triangle VUW\sim\triangle HGI \)