![]() A diagonal is perpendicular to another diagonal if the product of their slopes is -1. To prove that the diagonals of ABCD are perpendicular: Since opposite sides are parallel, ABCD is a parallelogram.Ģ. Now, let's find the slopes of BC and AD. Since the slopes are equal, AB and CD are parallel. We can find the slopes of AB and CD to check if they are equal. ![]() Recall that a parallelogram is a quadrilateral with opposite sides parallel. To verify that parallelogram ABCD is a rhombus, we need to show two things:ġ. Therefore, parallelogram ABCD is a rhombus, as it has both parallel sides and perpendicular diagonals. Since the product of the slopes of the diagonals is -1, we can conclude that the diagonals of ABCD are perpendicular. The product of the slopes of the diagonals AC and BD is (3/2) * (-2/3) = -1. The slope of diagonal BD can be calculated as: The slope of diagonal AC can be calculated as: To show that the diagonals of ABCD are perpendicular, we need to demonstrate that the product of the slopes of the diagonals is -1. Step 2: Prove that the diagonals of ABCD are perpendicular: Since the opposite sides AB and CD have the same slope of -7/4, and the opposite sides BC and AD have the same slope of -1/8, we can conclude that ABCD is a parallelogram. The slope of side AD can be calculated as: The slope of side BC can be calculated as: The slope of side CD can be calculated as: The slope of side AB can be calculated as: We can use the slope formula to find the slopes of the sides and compare them. In order to prove that a quadrilateral is a parallelogram, we need to show that opposite sides are parallel. Step 1: Prove that ABCD is a parallelogram: To verify that parallelogram ABCD is a rhombus, we need to show that it is a parallelogram with perpendicular diagonals.
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