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8.  What do you notice about the relationship among the areas of the polygons constructed on the sides of these right triangles? _______________________________________________________

Triangular dot paper is also called isometric dot paper since the dots are arranged in a triangular or isometric pattern. If you draw line segments connecting adjacent dots, then equilateral triangles are formed. On isometric dot paper, one linear unit is equal to the length of a side of the triangle (s = 1) while one area unit is equal to the area of an equilateral triangle: A = ¼·(√3).

On isometric dot paper, construct each set of polygons on the sides of the right triangles shown. Then find the areas of the polygons and record the data in the table.
Figure Area of shorter leg's polygon Area of longer leg's polygon Area of hypotenuse's polygon H I
11. What do you notice about the relationship among the areas of the polygons constructed? __________________________________________________________________
12. Does the same relationship hold for constructing polygons on the slides of a right triangle using square dot paper and isometric paper? Explain. __________________________________________________________________ __________________________________________________________________

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