Geometry Question Bank #2 Splitting Triangles

[tim]

ABC and BAC add up to 90 degrees (do you see why?)
ABC and ADC add up to 90 degrees (do you see why?)
that means BAC and ADC must be equal (do you see why?)

[003dnj]

Additionally, AC is the bisectrix of the angle BAD.

this is false.
if this were true, then you would have two 3-4-5 triangles back-to-back.
3-4-5 triangles don't have 45° angles, so, in that case, angle BAD wouldn't be a right angle.

There it is. Thank you.

[jnelson0612]

Great! :-)

[adm45]

For future problems, what method we should remember for future problems (my main concern is remember between 2 and 3). Given that Ron says knowing principle of what happens when height is drawn from right angle to hypotenuse is rarely tested, should we:

1) realize that Pythagorean theory can be used by setting up variables, or
2) memorize the last principle Ron provided: "(thing standing up)^2 = (product of two things in the bottom that share the same endpoint as the thing standing up)."
3) know what are the similar sides of the similar triangles( which I don't know if there is a hard rule to determine similar sides other than long explanation given by JadranLee. mgmat-25-question-bank-geometry-t331.html

To solve for the length of side CD, we can set up a proportion, based on the relationship between the similar triangles ACD and BCA: BC/AC = CA/CD

[tim]

I'm not sure what your question is in general, and what you mean by 2 and 3 in particular, but my generic advice would be to make sure you are familiar with all methods to solve any given problem.