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Rectangles

A rectangle is defined as a quadrilateral with two pairs of parallel sides and four right angles. To prove that the vertices A(6,0), B(3,9), C(-3,7), and D(0,-2) form a rectangle, we need to establish that opposite sides are parallel and consecutive sides are perpendicular. By calculating the slopes of sides AB, BC, CD, and AD, we can check for equality among opposite sides and opposite reciprocals among consecutive sides. This process confirms that ABCD is indeed a rectangle as it meets the necessary geometric conditions.

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Rectangles

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  1. Rectangles A rectanlgeis defined the following way: a quadrilateral that is made up of two pairs of parallel lines and that has four right angles To prove a quadrilateral is a rectangle, you must show that: 1) Opposite sides are parallel. 2) Consecutive sides are perpendicular. opposite consecutive consecutive opposite

  2. Rectangles Prove that A(6,0), B(3,9), C(-3,7), and D(0,-2) form a rectangle? 1) Show that opposite sides are parallel by showing the slopes are the same. 2) Show that consecutive sides are perpendicular by showing that the slopes are opposite reciprocals. Find the slope of AB, BC, CD, and AD. Slope of AB = Slope of BC = Slope of CD = Slope of AD =

  3. Rectangles JUSTIFICATION 1) Because the slopes of AB and CD are equal AND the slopes of BC and AD are equal, opposite sides are parallel. 2) a) The slopes of AB and BC are opposite reciprocals. Slope of AB = Slope of BC = b) The slopes of BC and CD are opposite reciprocals. c) The slopes of CD and AD are opposite reciprocals. Slope of CD = Slope of AD = d) The slopes of AD and AB are opposite reciprocals. THEREFORE, there are 4 right angles. Because opposite sides are parallel and there are 4 right angles, ABCD is a rectangle.

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