Final answer:
To show that triangles ABG and A1B1G are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional. After comparing the corresponding angles and sides, we can conclude that the triangles are similar, and the similarity statement is ABG ~ A1B1G.
Step-by-step explanation:
The triangles in question are ABG and A1B1G. To show that they are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.
From the given information, we can see that angle A is congruent to angle A1, angle B is congruent to angle B1, and angle G is congruent to angle G. Therefore, the corresponding angles are congruent.
Next, we compare the corresponding sides. We have AB/B1A1 = 5/24, AG/GG = 15/18, and BG/B1G = 16.5/5.5. Simplifying each ratio gives us AB/B1A1 = 5/24, AG/GG = 5/6, and BG/B1G = 3/1. Therefore, the corresponding sides are proportional.
Based on these congruent angles and proportional sides, we can conclude that triangles ABG and A1B1G are similar. The similarity statement for these triangles is ABG ~ A1B1G.