1. **Find the size of angle $\Theta$ to the nearest degree:** The problem gives two sides adjacent to $\Theta$ in a right triangle: opposite side length 21 cm and adjacent side length 30 cm formed the angle $\Theta$. 2. To find $\Theta$, we use the tangent function since $\tan \Theta = \frac{\text{opposite}}{\text{adjacent}}$. $$\tan \Theta = \frac{21}{30}$$ 3. Calculate the ratio: $$\tan \Theta = 0.7$$ 4. Find $\Theta$ by taking the arctangent (inverse tangent): $$\Theta = \tan^{-1}(0.7) \approx 44^\circ$$ --- 5. **State the Theorem that defines similarity of the given triangles:** The second problem compares two triangles with corresponding sides: - Triangle 1: 2.5 cm, 4.5 cm, 5 cm - Triangle 2: 6 cm, 10.8 cm, 12 cm 6. Check the ratios of corresponding sides: $$\frac{2.5}{6} = 0.4167,\quad \frac{4.5}{10.8} = 0.4167,\quad \frac{5}{12} = 0.4167$$ 7. Since all corresponding side ratios are equal, by the Side-Side-Side (SSS) Similarity Theorem, the triangles are similar. 8. The ratio of similarity is therefore $\frac{5}{12}$ or approximately 0.4167. **Final answers:** - Angle $\Theta \approx 44^\circ$ - Theorem: The Side-Side-Side (SSS) Similarity Theorem applies with similarity ratio $\frac{5}{12}$.