Question 453114
Isosceles triangle has two equal sides (legs) and third that we call base. 
Angles that base forms with legs are equal (congruent).
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In given triangle we have that height AD halves the angle in vertex A.
AD also forms two right triangles ABD and ACD. 
:
In these two triangles we have
angle BAD =  angle CAD, it is given
angle ADC = angle ADB, these two are right angles
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Now remaining angles ACD and ABD have to be also equal.
:
Since these two angles are equal it makes BC a base and BA and CA legs of isosceles triangle.