document.write( "Question 105263: How do I set up this proof, figure out a diagram, and givens?:
\n" ); document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #76620 by mbotros(2)\"\" \"About 
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Given
\n" ); document.write( "1- Draw Isosceles triangle ABC.
\n" ); document.write( "2- Divide each of the sides AB,AC,CA into two equal halfs.
\n" ); document.write( "3- Let point f be the midpoint of segement AC.
\n" ); document.write( "4- Let points d,g be the midpoints of sides BC and BA.
\n" ); document.write( "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
\n" ); document.write( "\n" ); document.write( "R.T.P: that 'Bf' is perpendicular to 'AC'.\r
\n" ); document.write( "\n" ); document.write( "Proof: Since ABC is Isosceles triangles then the measure of angle ABC equal to the measure of angle BCA.
\n" ); document.write( " 2- Side 'BA' equal To Side 'BC'.\r
\n" ); document.write( "\n" ); document.write( "Since the two triangles ABf and CBf are congruent we find that:
\n" ); document.write( "The measure of angle CfB equals to the measure of Angle AfB
\n" ); document.write( "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.
\n" ); document.write( " So, 'Bf' is perpendicular to 'AC'. \r
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