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How do you prove the hypotenuse leg theorem without using Pythagorean theorem?
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∙ 15y ago
I have to prove http://s5.tinypic.com/19ldma.jpg http://img22.imageshack.us/img22/9263/mathhlproofou4.jpg
without using pythagorean theorem
Wiki User
∙ 15y ago
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How does the pythagorean theorem prove irrational numbers?
It does not.If you consider a right angled triangle with minor sides of length 1 unit each, then the Pythagorean theorem shows the third side (the hypotenuse) is sqrt(2) units in length. So the theorem proves that a side of such a length does exist. However, it does not prove that the answer is irrational. The same applies for some other irrational numbers.
Does pythagorean theorem prove a triangle to be a right triangle?
Yes
What type of triangle proves the pythagorean theorerm?
The Pythagorean Theorem applies only to right triangles. (But they don't prove it.)
When did James Garfield prove the pythagorean theorem?
Somewhere around 1875 and 1876
How do you prove pythagorean theorom?
The law of cosines states that in any triangle, c2 = a2 + b2 - 2abcosy, where c is the hypotenuse, a and b are the legs, and y is the angle opposite c, the hypotenuse. Since in a right triangle, this is always 90 degrees, the cosine of y will always be 0. since 2ab(0) is 0, we get the formula a2 + b2 = c2, the Pythagorean Theorem.
How do you prove the pythagorean theorem?
For any right angle triangle its hypotenuse when squared is equal to the sum of its squared sides.
Why are there so many ways to prove the pythagorean theorem?
Because in a right angle triangle the square of its hypotenuse is always equal to the sum of each side squared.
How does the pythagorean theorem prove irrational numbers?
It does not.If you consider a right angled triangle with minor sides of length 1 unit each, then the Pythagorean theorem shows the third side (the hypotenuse) is sqrt(2) units in length. So the theorem proves that a side of such a length does exist. However, it does not prove that the answer is irrational. The same applies for some other irrational numbers.
Does pythagorean theorem prove a triangle to be a right triangle?
Yes
What type of triangle proves the pythagorean theorerm?
The Pythagorean Theorem applies only to right triangles. (But they don't prove it.)
When did James Garfield prove the pythagorean theorem?
Somewhere around 1875 and 1876
How do you prove pythagorean theorom?
The law of cosines states that in any triangle, c2 = a2 + b2 - 2abcosy, where c is the hypotenuse, a and b are the legs, and y is the angle opposite c, the hypotenuse. Since in a right triangle, this is always 90 degrees, the cosine of y will always be 0. since 2ab(0) is 0, we get the formula a2 + b2 = c2, the Pythagorean Theorem.
Can the Pythagoras theorem be proven emperically?
ANSWERYes The Pythagorean Theorem Can Be Proven Empirically.HOW?First, Lets Define The Theorem:In simplest terms, the Pythagorean Theorem is essentially a Formula that is TRUE for ANY/ALL RIGHT TRIANGLES (ANY Triangle that has ONE 90o ANGLE). The formula States: A2 + B2 = C2 , WHERE C is Always The Longest Side (Called The Hypotenuse) and is Always OPPOSITE the 90o Angle. A and B are The Other two sides of the triangle (not the Hypotenuse), the sides adjacent to the 90o Angle. To Prove The Pythagorean Theorem Empirically:First off lets define Empirically; all that it means, in this instance, is Show or Prove that the Theorem works through experience/experiment. This is very easy, just do the following: Using a protractor make a 90o AngleDraw 2 lines (Sides A & B) that make up the 90o Angle you measured out in Step 1Draw Side A - 5 cm in lengthDraw Side B - 8 cm in lengthDraw Side C - the Hypotenuse (A line that Connects Sides A and B) - But Do NOT Measure This with your ruler YET.Now since we need to PROVE that the Theorem is Correct, We have to Plug the length of the Sides A and B into the Theorem's Formula.52 + 82 = C2 (WHERE C2 is the Length of Side C/The Hypotenuse Squared)So Now we have the Equation: C2 = 25 + 64 = 89Now we need to Find what C equals, we do this by taking the Square Root of 89, and Since we know C is a Positive Number (Since its the Length of Side C), we can ignore the Negative portion of the Square Root and So We Know:C = 9.434 cmLAST STEP, NOW You MEASURE - with your Ruler, the Hypotenuse (Side C), and you will see that it equals 9.434 cm; therefore we have just Proved Empirically that the Pythagorean Theorem is Correct.
What are the theorems and postulates you can use to prove triangles are congruent?
Pythagorean's Theorem is one of the most famous ones. It says that the two squared sides of a right triangle equal the squared side of the hypotenuse. In other words, a2 + b2 = c2
True or false a theroem is a statement that can be easily proved?
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
How do you prove that a hypotenuse of a right triangle is the side of greatest measure?
For example, you can take a look at the Pythagorean formula: c = square root of (a2 + b2).
Why was Pythagorean Theorem become necessary to incorporate in the number system?
Your question is so confusing that I almost trashed it and am not sure yet what you want to know but I have a possible idea : consider a right triangle each of whose legs have length 1. By the Pythagorean theorem, the hypotenuse has length equal to the square root of 2. The square root of 2 is irrational- one can prove it is not equal to any fraction of integers, yet it is obviously is a number of some kind. Thus the number system had to be extended to include numbers of this kind.
