Question

are these scalene triangles similar?
u
35
s
45
t
j
72
i
56
h
yes
no

Explanation:

Step1: Identify included sides/ratios

Calculate ratio of corresponding sides:
$\frac{SU}{HI} = \frac{35}{56} = \frac{5}{8}$
$\frac{UT}{HJ} = \frac{45}{72} = \frac{5}{8}$

Step2: Check included angles

The marked angles at $U$ and $H$ are equal.

Step3: Apply SAS similarity

Since two sides are in equal ratio, and included angles are congruent, the triangles are similar by SAS Similarity Criterion.

Answer:

yes