Definition: A triangle is isosceles if two of its sides are equal.
Theorem: Let ABC be an isosceles triangle with AB = AC. Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC). Then
Ray AM is the angle bisector of angle BAC.
Line AM is the altitude of triangle ABC through A.
Line AM is the perpendicular bisector of B
Segment AM is the median of triangle ABC through A
If |AB| is not equal to |AC| then D is not the midpoint of BC so this method doesn't work. In this case you can use trigonometry. The sine of the angle at B is |AD|/|AB| and thus http://www.k6-geometric-shapes.com/isosceles-triangle.html
|AD| = |AB| sin(B) 
Theorem: Let ABC be an isosceles triangle with AB = AC. Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC). Then
If |AB| is not equal to |AC| then D is not the midpoint of BC so this method doesn't work. In this case you can use trigonometry. The sine of the angle at B is |AD|/|AB| and thus http://www.k6-geometric-shapes.com/isosceles-triangle.html
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