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.)
answer attempt 1 out of 2
the triangles
✓ similar.

Explanation:

Step1: Identify side lengths of triangles

Triangle PQR: $PQ=19$, $QR=19$, $PR=25$
Triangle STU: $ST=76$, $TU=76$, $SU=100$

Step2: Calculate side length ratios

$\frac{PQ}{ST} = \frac{19}{76} = \frac{1}{4}$
$\frac{QR}{TU} = \frac{19}{76} = \frac{1}{4}$
$\frac{PR}{SU} = \frac{25}{100} = \frac{1}{4}$

Step3: Check similarity condition

All corresponding side ratios are equal, satisfying the SSS (Side-Side-Side) similarity criterion.

Answer:

The triangles are similar, by the SSS (Side-Side-Side) similarity criterion (all corresponding side lengths are in the same ratio of $\frac{1}{4}$).