Question

determine if triangle $pqr$ and triangle $stu$ are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
the triangles $square$ similar.
answer
are
are not

Explanation:

Step1: Match corresponding sides

Triangle PQR sides: $PQ=11$, $PR=15$, $QR=17$
Triangle STU sides: $ST=55$, $SU=75$, $TU=85$

Step2: Calculate side ratios

$\frac{ST}{PQ} = \frac{55}{11} = 5$
$\frac{SU}{PR} = \frac{75}{15} = 5$
$\frac{TU}{QR} = \frac{85}{17} = 5$

Step3: Check similarity condition

All corresponding side ratios are equal.

Answer:

The triangles are similar, by the Side-Side-Side (SSS) similarity criterion (all corresponding sides are in proportion with a scale factor of 5).