SOLUTION: Please help me with this problem. If a median is also an altitude of a triangle, prove the triangle is isosceles.

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Question 387958: Please help me with this problem. If a median is also an altitude of a triangle, prove the triangle is isosceles.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the strategy is:

given ___ median and altitude

median divides side into equal lengths

altitude is perpendicular

the median equals itself (reflection)

the two right angles from the perpendicular are equal

the two halves of the side divided by the median are equal (definition of median)

so the two internal triangles are congruent by SAS

the two sides of the larger triangle are congruent (CPCTC)

the large triangle is isosceles by definition