A Geometry student says I got lost in that lesson I wrote down that AD/AB eQUALS AC/ab but I have no idea where comes from

AD/AB = AB/AC

Step-by-step explanation:

If we take two triangules in that figure: ABC and ABD, both are triangles rectangles. We need to use the definition of cosine, with the angle in th A corner, we called ∅.

For the ABC triangle: cos(∅) = adjacent cathetus/hypotenuse = AD/AB

For the ABD triangle: cos(∅) = adjacent cathetus/hypotenuse = AB/AC

Then:

cos(∅) = AD/AB = AB/AC