Pythagorean theorem

Example: A Let's check if the areas are the same: 3 2 + 4 2 = 5 2 Calculating this becomes: 9 + 16 = 25 It works ... like Magic! Why Is This Useful? If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!) How Do I Use it? Write it down as an equation: And You Can Prove The Theorem Yourself ! Get paper pen and scissors, then using the following animation as a guide: • Draw a right angled triangle on the paper, leaving plenty of space. • Draw a square along the hypotenuse (the longest side) • Draw the same sized square on the other side of the hypotenuse • Draw lines as shown on the animation, like this: • • Cut out the shapes • Arrange them so that you can prove that the big square has the same area as the two squares on the other sides Another, Amazingly Simple, Proof Here is one of the oldest proofs that the square on the long side has the same area as the other squares. Watch the animation, and pay attention when the triangles start sliding around. You may want to watch the animation a few times to understand what is happening. The purple triangle is the important one. becomes We also have a

Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas. Let us learn the mathematics of the Pythagorean theorem in detail here. Pythagoras Theorem Statement Pythagoras theorem states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple. History The theorem is named after a Greek Mathematician called Pythagoras. Pythagoras Theorem Formula Consider the triangle given above: Where “a” is the perpendicular, “b” is the base, “c” is the hypotenuse. According to the definition, the Pythagoras Theorem formula is given as: Hypotenuse 2  = Perpendicular 2  + Base 2  c 2  = a 2  + b 2   The side opposite to the right angle (90°)  is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest. Consider three squares of sides a, b, c mounted on the three sides of a triangle having the sa...

The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent). Once you progress, you will be given the hypotenuse and would be needed to find the opposite or the adjacent side (a or b). The Pythagorean theorem is a simple formula which uses the squared value of a and b; for example "a=3 and b=4, what is the value of c?" you square a (3^2=9=a) and b (4^2=16=b) and add the 2 values (9+16=25) to get to c. To complete the question, you have to square root c's value (square root of 25=5) because the formula says c^2 and not just c. Once you have done that, you can check your answer by squaring a,b and c to see if you have added and divided (Square-rooted) correctly. Hope this helps! 5:27 he said that in order to complete the equation you have to take the positive square root of both sides, which for 25 would equal 5. But what does that mean? How did he get 5 from 25? What did he do, what did he divide 25 by and why did he divide that and not another number? I will be waiting for a response thank you to those that reply, I will be very thankful because I know I would be taking time away from you just so you can answer my question. Thanks! A square root is a number that produces a specified quantity when multiplied by itself. It goes hand in hand with exponents and squares. 2 squared is 4, and the square root of 4 ...