Question

determine if triangle mno and triangle pqr 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: Find $\angle O$ in $\triangle MNO$

Sum of angles in a triangle is $180^\circ$.
$\angle O = 180^\circ - 52^\circ - 67^\circ = 61^\circ$

Step2: Compare side ratios

Match sides around equal $\angle M$ and $\angle P$:
$\frac{MN}{PR} = \frac{19}{40} = 0.475$, $\frac{MO}{PQ} = \frac{20}{39} \approx 0.513$

Step3: Check SAS similarity rule

Equal included angles ($52^\circ$), but side ratios are not equal. Also, no matching equal angle pairs for AA similarity.

Answer:

The triangles are not similar.