SOLUTION: How do I set up this proof, figure out a diagram, and givens?: The line drawn from the vertex angle of an isosceles triangle through the point of intersection of the medians to th

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Question 105263: How do I set up this proof, figure out a diagram, and givens?:
The line drawn from the vertex angle of an isosceles triangle through the point of intersection of the medians to the legs is perpindicular to the base.
Answer by mbotros(2) About Me  (Show Source):
You can put this solution on YOUR website!
Given
1- Draw Isosceles triangle ABC.
2- Divide each of the sides AB,AC,CA into two equal halfs.
3- Let point f be the midpoint of segement AC.
4- Let points d,g be the midpoints of sides BC and BA.
5- Join Bf,Cg,Af they will meet at the point 'm'(the point at which the three medians meet and it is called Centroid)
R.T.P: that 'Bf' is perpendicular to 'AC'.
Proof: Since ABC is Isosceles triangles then the measure of angle ABC equal to the measure of angle BCA.
2- Side 'BA' equal To Side 'BC'.
Since the two triangles ABf and CBf are congruent we find that:
The measure of angle CfB equals to the measure of Angle AfB
But The angle CfA is straight angle and it's measure equal to 180 degrees Then we conclude that angle CfB equals to AfB equal to 180/2 equals to 90 degrees.
So, 'Bf' is perpendicular to 'AC'.