Question

are these shapes similar?
(there are two triangles in the image, with side lengths and angles marked. options: yes, no, and a submit button.)

Explanation:

Step1: Match corresponding sides/angles

In $\triangle QRS$: $\angle Q$ corresponds to $\angle V$, $\angle R$ corresponds to $\angle X$, $\angle S$ corresponds to $\angle W$.
Side $QS=52$ in corresponds to $WV=32$ in, side $QR=52$ in corresponds to $VX=43$ in, side $RS=32$ in corresponds to $XW=40$ in.

Step2: Check side ratios

Calculate ratio of $QS$ to $WV$: $\frac{52}{32} = \frac{13}{8} = 1.625$
Calculate ratio of $QR$ to $VX$: $\frac{52}{43} \approx 1.209$
Calculate ratio of $RS$ to $XW$: $\frac{32}{40} = \frac{4}{5} = 0.8$

Step3: Verify similarity condition

For triangles to be similar, all corresponding side ratios must be equal, or corresponding angles must be equal (AA similarity). The side ratios are not equal, and the marked angles do not form a matching AA pair (the equal angles are not in corresponding positions to satisfy AA).

Answer:

no