Question 204123
Triangle,,,ABC,,altitude  AD, AB=AC=5,,,,,all  GIVEN
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AD perpendicular  to  BC,,,,,,,,,,,,,,,,Def  of  Altitude
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ABD,,,and  ACD  are  right  triangles,,,,,,,,,def  of  rt  triangle
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AD =AD,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Same  Line
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AB^2 -AD^2 = BD^2,,,,,,,,,,,,,,,,,,Pythagorean  Theorem
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AC^2 -AD^2 = CD^2,,,,,,,,,,,,,,,,,,Pythagorean  Theorem
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BD^2 =CD^2,,,,,,,,,,,,,,,,,,,,,,,,,arithmetic  and  substitution(AB+AC)
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BD = CD,,,,,,,,,,,,,,,,,,,,,,,,,,,,square  root
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Therefore  AD,  bisects  BC,,,,,,,,def  of  bisector
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