1. **Stating the problem:** Determine whether the given pairs of triangles are similar or not, and if similar, identify the similarity criteria. 2. **Similarity criteria for triangles:** Triangles are similar if they satisfy one of the following: - Angle-Angle (AA): Two angles of one triangle are equal to two angles of another. - Side-Angle-Side (SAS): Two sides are proportional and the included angle is equal. - Side-Side-Side (SSS): All three sides are proportional. 3. **First pair: $\triangle XYZ$ and $\triangle YNM$** - Given: Right angles at $X$ in $\triangle XYZ$ and at $N$ in $\triangle YNM$. - Both have a right angle, so one angle is equal. - If another angle is equal, then by AA, triangles are similar. - Since $YZ$ is the hypotenuse in $\triangle XYZ$, check if corresponding sides are proportional. - Without side lengths, we cannot confirm similarity; thus, they are **not necessarily similar**. 4. **Second pair: $\triangle ABC$ and $\triangle DEF$** - Sides of $\triangle ABC$: 12 (AC), 8 (AB), 6 (BC) - Sides of $\triangle DEF$: 3 (ED), 6 (EF), 4 (DF) - Check side ratios: $$\frac{12}{3} = 4, \quad \frac{8}{6} = \frac{4}{3}, \quad \frac{6}{4} = 1.5$$ - Ratios are not equal, so by SSS, triangles are **not similar**. 5. **Third pair: $\triangle SQU$** - Given sides: $SQ = 10$, $QU = 25$, angle at $Q$ marked. - No second triangle given for comparison, so similarity cannot be determined. **Final answers:** - $\triangle XYZ$ and $\triangle YNM$: Not necessarily similar - $\triangle ABC$ and $\triangle DEF$: Not similar - $\triangle SQU$: Insufficient information to determine similarity