CONCLUSION: 3.4 Do you think that the previous RATIOS will always be the same for THE SAME ANGLE SIZES even if the triangles differ in sizes? Explain your answer. [3]

Absolutely! When it comes to triangles, the ratios of the sides indeed remain consistent for the same angle sizes, regardless of the triangle’s size. This stems from the principle of similarity: all triangles with the same angles are similar, meaning their corresponding sides are proportional. So, if you double the size of a triangle, the side lengths scale up by the same factor, but the angle ratios remain untouched. Additionally, this fascinating phenomenon is tied to the concept of trigonometric functions. For any given angle in a triangle, the sine, cosine, and tangent ratios are defined based on the lengths of the sides. Because these ratios are intrinsic to the angles themselves, they'll consistently produce the same values as long as the angles stay constant, yielding the same ratios no matter how you size up your triangles.