The Department of Mathematics and Science Education

tiffani c. knight

For this assignment, I had to show a proof of Ceva’s Theorem. According to my friends at http://en.wikipedia.org/wiki/Ceva’s_theorem , given a triangle ABC, and points D, E, and F that lie on lines BC, CA, and AB respectively, Ceva’s Theorem states that lines AD, BE, and CF are congruent if and only if

AF * BD * CE = 1

FB DC EA.

My friends at wikipedia.org also divulged that there is an equivalent trigonometric form of Ceva’s Theorem: AD, BE, CF concur if and only if

I am going to try to prove Ceva’s Theorem using the trig form.

So, does (.62/.52) * (.63/.52) * (.28/.40) = 1?

Well, let’s calculate and see. (I went back to the good ol’ TI 83 for this one). I got 1.01, which is pretty darn close if you ask me.

I went back and calculated the sine of each angle measurement without rounding like above and I got .9996947883. Again, that’s pretty darn close if you ask me.

We would get even more accurate, I bet, if we recalculated the angle measures and didn’t round off until the millionth or ten millionth place value. But we won’t do that. Two results of “pretty darn close” is good enough for me.