Pythagorean Threorem Spiral Project

THE PYTHAGOREAN THEOREM SPIRAL PROJECT The Pythagorean Theorem Spiral project involves creating a set of right triangles by using the hypotenuse of one triangle as the leg of the next triangle. In the video you watched, the teacher created a spiral with 35 triangles. In this project, create 17 right triangles that make up one spiral revolution. Calculate the hypotenuse of each triangle and place the information into the table. Finally, decorate the spiral in a unique and creative way. Materials needed: * Pencil * Pen or Marker * Notebook Paper * White Computer Paper * Compass * Protractor * Ruler * Coloring Supplies How to Draw a Pythagorean Theorem Spiral: First Starting Point Locate the first starting point by placing the computer paper in landscape orientation. Measure 15 cm to the right and 10 cm down from the top left corner of the computer paper and mark the first starting point. All the triangles will connect to this point. Measure very accurately to ensure the spiral will fit on the paper. First Right Triangle Create a drawing of the first triangle by measuring a segment from the first starting point. Draw a horizontal segment 3 cm to the left of the point and a vertical segment 3 centimeters up from the point as shown below. Be sure these segments are parallel and perpendicular to the edges of the paper. These will be the legs of the first right triangle. Connect the endpoints of the segments to form the hypotenuse of the first right triangle. 8cm Pythagorean Theorem Spiral Formation Step I: Form a new right triangle using the hypotenuse of the old right triangle as a leg of the next right triangle. Step II: Use the compass to copy the 3 cm segment (old side “b”) to form a leg attached to the hypotenuse of the old triangle. Measure the leg to verify it is 3 cm with a ruler to check your compass constructions. Use a protractor to measure the angle of the new leg so that it is perpendicular (90 degree angle) to the right side of the old hypotenuse. Be sure to use a ruler or other straightedge to draw the lines neat and professional looking. Step III: Connect that new leg (new side “b”) to the first starting point to form the hypotenuse of the new right triangle. Step IV: These three segments becomes the new triangle in the spiral. Continue the Pattern Repeat Steps I to IV to continue to create triangles in the spiral. Create a total of 17 triangles, which is one full revolution of the spiral. Be Creative Color the spiral to form more images and patterns. For ideas, Google “Pythagorean Theorem Spiral Project” and click on “Images.” Scroll through the pictures to see what other students have made. Do not copy anyone’s work, but use the ideas to inspire a unique and creative spiral. Do the Math Calculate the length of the hypotenuse in each of the 17 right triangles. Show the work on the notebook paper and attach it to the back of this project. All answers must be in their most reduced forms. Here is the first one done for you. Helpful Hints: • • • Complete assignment in pencil first, then mark over the lines using a pen or marker. Use a ruler to make the diagram neat and professional looking. Use the geometry tools (compass, protractor, and ruler) to measure very accurately and check your work after each step.