SOLUTION: What must I show to prove the theorem given below?: The median drawn to the base of an isosceles triangle bisects the vertex angle. (Basically, picture an isosceles triangle wi

Question 741823: What must I show to prove the theorem given below?:
The median drawn to the base of an isosceles triangle bisects the vertex angle. (Basically, picture an isosceles triangle with sides AB and AC congruent, and X bisects the triangle, cutting it in half, so that BX is congruent to XC.)
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
AB is congruent AC - Definition of an Isosceles triangle

BX is congruent to XC - Definition of a bisector

AX = AX - Reflexive property of equality (draw lines over the AX)

AX congruent to AX - definition of congruent.

Triangle ABX congruent to triangle ACX - SSS

Angle BAX congruent angle CAX - CPCTC (corresponding parts of congruent triangles are congruent

AX bisects angle BAC - Definition of angle bisector.

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