You can use Stewart's theorem.
Hi, i am having trouble with this proof. I have found mulitple webpages on the theorem, but not one of them i coudl find offers me a 'how to'
It is to do with Appolonis' Theorem. The question is:
"In triangle ABC, D is the midpoint of BC, then prove that -
AB² + AC² = 2AD² + 2CD²
Hint: Use Pythagoras' Theorem."
although from looking at the web, i am thinking my teacher has copied it down incorrectly since they all seem to say AB² + AC² = 2AD² + (BC²)/2
since AD is a median, and it is not known that there are any right angles in this triangle, i am not sure how to get Pythagoras in there at all
thanks for any help
jacs
Hello, jacs!
In is the midpoint of .
Prove that: .
We have: . with median .
Let .
Drop perpendicular from vertex to side . .Let .
.Let , then:In right triangle . [1]Code:A * *:* * * : * * * : * * * : * * * :h * * * : * * * : * * B * - - - + - - - * - - - - - - - * C x-a E a D x
In right triangle . [2]
Add [1] and [2]: .
And we have: . . [3]
. . In right triangle
. . . . We also know that:.
Therefore, [3] becomes: .