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Within a real world context (a city manager trying to plan shorter roads) students will produce diagrams of right triangles with rulers and find the relationship between the sides of the triangles. By the end of the lesson, students should see that the sum of the squares of the legs is equal to the square of the hypotenuse. Further, they should be able to produce the Pythagorean Theorem through class discussion. A teacher's guide is included.

Proof can be difficult to help students understand, but this activity walks them through two separate proofs of the Pythagorean Theorem, both of which are simple yet elegant. Students should experience success with proving the Pythagorean Theorem, a target that can be tough to accomplish!

After learning the transformations of translation, dilation, reflection, and rotation, students are challenged to plot an original image, then do all four transformations to it consecutively.