Answer:
4/8 = 5/10 = 6/12
Explanation:
The fill-ins you are looking for have to do with the picture of the triangles on the left, that has the side measure information.
The picture on the right with the angle measures is important too, for understanding "similar". All three angles in one triangle have to be the same three angles in the other triangle. Important, but we don't need it for the fill-in-the-blank question.
So, look at the picture on the left. There's two triangles, a big one and a little one. In the problem, in the purple writing it says "least to greatest, new over old, right over left"
The direction that says "least to greatest" is talking about the measures of the sides (look at the small triangle, for example) the three sides are 4, 5, and 6. So you're going to do something with the 4 first bc its the "least" (smallest) and next the side 5, and last the side 6 (bc its the biggest).
In the picture on the left the small triangle is the "new" and the big triangle is the "old".
In these purple directions, "left" and "right" refer to the two triangles in the left image. "Left" is the big triangle on the left (in the left image) "Right" is the small triangle on the right (in the left image).
Okay, so if the purple writing was causing confusion, they were really trying to give hints.
The side 4 in the small triangle, corresponds to the side 8 in the big triangle. They want you to write this ratio 4/8 (that IS new/old and right/left and it goes first bc its the smallest side)
Next comes 5/10.
Last is 6/12.
Besides having three angles the same, in order to be "similar" the ratios of the sides have to be the same ratio.
4/8 and 5/10 and 6/12 are all equal to each other. They all equal 1/2. So the ratios are equal to each other. So these triangles are similar.