SOLUTION: I need help writing a coordinate proof for the statement: The segments joining the vertices to the midpoints of the legs of an isosceles triangle are congruent. I cannot figure out

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Question 510285: I need help writing a coordinate proof for the statement: The segments joining the vertices to the midpoints of the legs of an isosceles triangle are congruent. I cannot figure out how to start it off as to what would be my Given and what i'm trying to prove.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
To construct a coordinate proof, you will have to fix points first. Without loss of generality suppose that for isosceles triangle ABC, A is at (0,0), B is at (2a,0), and vertex C is at (a,b) (so that AC = BC).

Let D and E be the midpoints of AC and BC respectively. We want to prove that BD = AE. We can easily find the coordinates of D and E using the fact that they're midpoints:





Then the distance from B to D is

(using the distance formula/Pythagorean theorem)

Similarly, the distance from A to E is the same amount. Hence BD = AE, and we are done.