Question

I always have trouble with these types of questions. Can someone explain how to do this? {Geomtry}

Answer 1

One good thing to remember about right triangles is that when an altitude is created in a right triangle, the two smaller triangles that it makes are both similar to the original triangle.  Review the properties of similar triangles and see if you can apply them to the four statements that are your answer options.

Answer 2

We know that because of line CD, these 2 trangles are similar. That means we can redraw triangle ADC to look like triangle CDB. In doing so, we can finally set up these proprtions to the leg lengths.
Another way to think of this is to just seperate the two triangles as they are, and rotate triangle ADC 90° clockwise in order to set up the proportions.
I hope this helped, it was hard to explain without visuals