Question 1022026
looks like this is an isosceles triangle but let's use the distance formula to determine the length of each side.
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d1 = square root( (0-(-a))^2 + (b - 0)^2 ) = square root( a^2 + b^2)
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d2 = square root( (0-a)^2 + (b-0)^2 ) = square root( a^2 + b^2)
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d3 = square root( (a-(-a))^2 +(0-0)^2 ) = square root( (2a)^2)
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d1 = d2, so we do have an isosceles triangle
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d1 and d2 are adjacent sides, so the median bisects the angle between them and also bisects the base of the triangle
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let D be the point of intersection on the base with the median
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the two triangles are congruent by SAS
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the two angles on ether side of the median at D are co-linear (they sum to 180 degrees) and they are equal because of congruence
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therefore the median is perpendicular at D
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