What does it mean in geometry when they are putting segments over each other to show proportionality? In some video about triangle proportionality theorem, he says "BA to the length of MA " then draws BA over MA like a fraction. What does he mean "to the length of"

Read below.

Step-by-step explanation:

The expression "BA to the length of MA" is probably part of the expression "the length of BA to the length of MA" and is a ratio.

A proportion is setting two ratios equal.

If two triangles are similar, then the lengths of corresponding sides are proportional. That means that the ratios of the lengths of corresponding sides are equal.

For example, let's say you are given triangles ABC and XYZ, and you are told that triangle ABC is similar to triangle XYZ.

By the order of the letters in ABC and XYZ, you can conclude that

side AB corresponds to side XY

side AC corresponds to side XZ

side BC corresponds to side YZ

Since the lengths of corresponding sides are in the same ratio, so you can further conclude that

the length of AB is to the length of XY as

the length of AC is to the length of XZ as

the length of BC is to the length of YZ

Mathematically, you can write the previous three lines as the proportion

AB/XY = AC/XZ = BC/YZ

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.