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The Pythagorean Theorem

Discover the Pythagorean Theorem through an investigation of right triangles and the squares built on each side. Apply the theorem to real-world problems and calculate lengths of legs and hypotenuse.

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The Pythagorean Theorem

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  1. The Pythagorean Theorem To discover the Pythagorean Theorem by exploring right triangles and the squares built on each side To apply the Pythagorean Theorem to real-world problems

  2. The Sides of a Right Triangle • This investigation will help you discover a very useful formula that relates the lengths of the sides of a right triangle.

  3. Draw a right triangle on graph paper with its legs on the grid lines and its vertices at grid intersections. • Draw a square on each side of your triangle. • Find the area of each square and record it. • As a group or as a class, combine your results in a table like this one. Look for a relationship between the numbers in each row of the table.

  4. Calculate the lengths of the legs and the hypotenuse for each triangle based on the areas you calculated in Step 3. • Use what you discovered about the areas of the squares to write a rule relating the lengths of the legs to the length of the hypotenuse.

  5. Example A • A baseball diamond is a square with 90 ft between first and second base. What is the distance from home plate to second base?

  6. Example B • Martin Weber is building a wheelchair ramp at the Town Hall. The ramp will start at ground level and rise to meet a door that is 30 in. off the ground. • Building codes in his area require an exterior ramp to have a slope of 1:12, meaning 1 in. of rise for every horizontal 12 in. • What will be the length of the ramp’s surface? • Give your answer in exact form and as an approximation to the nearest inch.

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