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Big Ideas:
The orientation of the object does not change the other attributes of the object.
Shapes can be transformed into similar shapes with proportional corresponding sides and congruent corresponding angles.
This lesson uses the area model of the Pythagorean Theorem as the base to develop a fractal. The task is to construct a fractal from either an isosceles right triangle and its corresponding squares of the sides or from a scalene right triangle and its corresponding squares of the sides. Starting with either right triangle, students will use one side of each of the squares on the legs of the original triangle to be the hypotenuses of the next right triangles in the iteration. Similar squares will be constructed off the legs of each of these triangles. New similar triangles will then be constructed on the sides of the squares of the legs of the second iteration triangles. The students will continue the pattern for at least seven iterations. During this process, students will see that the orientation of the shapes does not change their basic properties. Each fractal creates a series of triangles and squares that are mathematically similar to the original triangle and squares of its sides.
Vocabulary:
right triangle, hypotenuse, leg, fractal, iteration, scalene, isosceles
Special Materials:
ruler
protractor
isometric dot paper
plain paper
geometric software (optional)