SOLUTION: Given a triangle ABC with an altitde AD and sides AB and AC measuring 5 units, prove that AD bisects BC.

Question 204123: Given a triangle ABC with an altitde AD and sides AB and AC measuring 5 units, prove that AD bisects BC.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
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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