Pythagorean Theorem (a2+b2=c2 ) is a classic equation which defines the relation among the three sides of a right angle triangle. This equation can be effectively proven by practicing Extended Side Angle pose (utthita parsvakonasana). This is also a wonderful way to incorporate kinesthetic learning into a sometimes challenging algebraic concept helping all students to solidify their understanding through whole body integration.
With a partner use the Pythagorean Theorem to find the length of your hypotenuse (the longest side of the triangle) with one person performing the pose, and other measuring the distance from the tips of the fingers straight down to the floor (the height) and the distance between the feet (the base). Next measure from the tips of the fingers along the length of the body to the end of the toes (the hypotenuse) to verify your answer. Switch roles and repeat.
Once you have these measurements you can delve deeper into understanding the geometry of a right angle triangle by performing these calculations.
- Calculate the perimeterof your triangle by adding the length of the three sides: a+b+c = perimeter
- Calculate the area of your triangle: 1/2(base x height) = area
Calculate the height of your triangle when using the hypotenuse as the base in your calculations. You may have to sketch a scale drawing of the triangle to perform these calculations, flipping the triangle so that the hypotenuse is the base to make it visually easier to understand. This step will involve some understanding of sine and angles and is more advanced than the previous calculations.
Finally make a chart of the different calculations including diagrams to reinforce visual understanding.
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