Question 549203
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

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