Derive the Pythagorean Theorem. Show steps along the way. Thanks

Pythagorean Theorem In any right triangle, the sum of the square of the two perpendicular sides is equal to the square of the longest side. For a right triangle with legs measures a and b and length of hypotenuse c, the theorem can be expressed in the form: c^2=a^2+b^2 see attached: Area of the large square = Area of four triangles + Area of small square A[total]=A[four-triangles]+A[small square] (a+b)^2=4((1/2)ab)+c^2 a^2+2ab+b^2=2ab+c^2 a^2+b^2=c^2

In trigonometry, we'll discuss triangles that are not right triangles. Trigonometry is still many chapters away in the Ron Larson textbook.