Proof (synthetic): Through a vertex, draw a line parallel to the opposite side. Alternate interior angles give the sum of the three angles as a straight angle.
( a + b > c ), ( a + c > b ), ( b + c > a ), with equality degenerate.
A parallelogram is a rhombus iff diagonals are perpendicular or one diagonal bisects an interior angle.
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Proof (synthetic): Through a vertex, draw a line parallel to the opposite side. Alternate interior angles give the sum of the three angles as a straight angle.
( a + b > c ), ( a + c > b ), ( b + c > a ), with equality degenerate.
A parallelogram is a rhombus iff diagonals are perpendicular or one diagonal bisects an interior angle.
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