SOLUTION: what is the answer to this proof? Given:Isosceles triangle with a bisector of the vertex angle Prove: The vertex angle bisector is perpendicular to the base of the isosceles tria

Question 549203: what is the answer to this proof?
Given:Isosceles triangle with a bisector of the vertex angle
Prove: The vertex angle bisector is perpendicular to the base of the isosceles triangle
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let the angle bisector of BAC intersect segment BC at point D.
Since ray AD is the angle bisector, angle BAD = angle CAD.
The segment AD = AD = itself.
Also, AB = AC since the triangle is isosceles.
Thus, triangle BAD is congruent to CAD by SAS Test.
Therefore triangle BAD = triangle CAD, and corresponding sides and angles are equal.
DB = DC,
angle ABD = angle ACD
angle ADB = angle ADC. From congruence of triangles, angle ADB = angle ADC. But by addition of angles, angle ADB + angle ADC = straight angle = 180 degrees. Thus 2 angle ADB = straight angle and angle AMB = 90 degrees = right angle.
QED
m.ananth@hotmail.ca

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