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Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals.

Mathematics
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So first you need to show it is a parallelogram. You do that by showing opposite sides are parallel. You do that by showing that they have the same slopes. (or if you know vectors by showing the sides point in the same direction). Next you need to show the diagonals are perpendicular. Do you that by showing the slopes of the diagonals have the characteristic of perpendicular lines: i.e., the product of their slopes is -1. But the thing you should do before either of those steps, call it "Step Zero" is draw a diagram. Draw a diagram of the figure by sketching out the location of the four vertices and the sides between them.
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