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# Francesca is writing a coordinate proof to show that the diagonals of a rectangle divide the rectangle into four triangles of equal area.

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Francesca is writing a coordinate proof to show that the diagonals of a rectangle divide the rectangle into four triangles of equal area.

Enter your answers in the boxes to complete Francesca's proof. Since PQRS is a rectangle, the coordinates of R are (_____, 2y). Since diagonals of a rectangle bisect each other, the coordinates of T are (x, ____). In △PTS, the length of the base is 2x and the height is y. So an expression for the area of △PTS is ​ xy ​ . In △PTQ, the length of the base is 2y and the height is x. So an expression for the area of △PTQ is ______. In △RTQ, the length of the base is ______ and the height is y. So an expression for the area of △RTQ is xy . To find the area of △RTS, the length of the base is 2y and the height is ______. So an expression for the area of △RTS is ​ xy ​ . Comparing the four areas shows that the diagonals of a rectangle divide the rectangle into four triangles of equal areas.

Oct 1, 2018