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# Mason loosleandresantos honors geometry project

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### Mason loosleandresantos honors geometry project

1. 1. The picture below shows the formula for thePythagorean theorem. In the picturebelow, side C is always the hypotenuse.Remember that this formula only applies toright triangles. c A² + B² = C² a b
2. 2. The Triangle below is a 3,4,5 A² + B² = C² 3² + 4² = 5² 9 + 16 = 25Image taken from:http://www.mathsisfun.com/pythagoras.html
3. 3. Step 1) Identify the legs and the hypotenuse of the right triangle.The legs have length 6 and 8 . X is the hypotenuse because it is opposite the rightangle.Step 2) Substitute values into the formula (remember c is the hypotenuse)A2 + B2 = C262 + 82 = X2Step 3) Solve for the unknown6²+8²=x²100=x²√100=x xX=10 6 8
4. 4. Step 1) Identify the legs and the hypotenuse of the right triangle. The legs have length 24 and X are the legs. The hypotenuse is 26.Step 2) Substitute values into the formula (remember c is the hypotenuse)A2 + B2 = C2x2 + 242 = 262Step 3) Solve for the unknown x²+24²=26² x²+576=676 x²=676-576 x²=100 x=√100 26 x=10 x 24
5. 5. c²=a²+b²The converse of the Pythagorean Theoremhelps you to find out if a triangle is right.Basically, the converse states thatwhenever the sum of the squares of twosides equal to the square of the third sideof the triangle, the triangle is a righttriangle
6. 6. Do the sides 6, 8, and 10 form a righttriangle?Is 102 = 62 + 82 ?102 = 100 and 62 + 82 = 36 + 64 = 100Since 100 = 100, the triangle is a righttriangle.