Question

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

https://static.k12.com/nextgen_media/assets/8080686-NG_GMT_SemA_IT_02_11.png

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.

Answer 1

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