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May 04, · The Pythagorean Theorem states that the sum of squares of the two legs of a right triangle is equal to the square of the hypotenuse, so we need to prove a2 + b2 = c2. Remember, 66%(91). Pythagorean Theorem Algebra Proof What is the Pythagorean Theorem? You can learn all about the Pythagorean Theorem, but here is a quick summary: The Pythagorean Theorem says that, in a right triangle, the square of a (which is a?a, and is written a 2) plus the square of b (b 2) is equal to the square of c (c 2): a 2 + b 2 = c 2. Proof of the Pythagorean Theorem using Algebra.

Pythagorean Theorem is a widely used theorem in math and geometry with many applications. It shows the relationship of the 3 sides of a right triangle. It is used so much, that it is hard to not know it. However, many students just know it as how to filter sediment out of wine is. They never know how to prove it.

How do you know Pythagorean Theorem formula is true? Today we are going to show you, with the toy you have at home, LEGO. Created by my son, this is the easiest proof of Pythagorean Theorem, so easy that a 3rd grader will be able to do it. Sometimes kids have better ideas, and this is one of them.

To prove Pythagorean Theorem following the strict mathematics method, some one needs understand many advanced math concepts first, such as square root. For elementary students who have no knowledge of these concepts, it is hard to understand the mathematic simole of the theorem. However, many schools instroduce Pythagorean Theorem at elementary school level.

To avoiding confusing kids, it goes without a proof. It is just introduce as it is. All they need know is the area of a square, which is the product of the two sides. Since the two sides are the same length for the square shape, it is square of the sides. As show in the equation, Pythagorean Theorem is about the relationship among the 3 sides of a right triangle. To prove the Pythagorean Theorem, we just need prove the sum of the areas of square A and square B is equal to the area of square C.

Luckily, there are so many research on Pythagorean Theorem, a quick search on Google can give us many of these square triples. To save your time, I have listed out all 16 primitive Pythagorean Pythaboras under Yes, there are just 16 primitive triples under You can download the list, together with a LEGO somple template at the bottom of this post. I will explain about the template shortly. An example is 3, 4, 5.

They are also Pythagorean triples. But they are not primitive triples, since they are multiple of 3, 4, 5. Smple you know, besides the primitive triples, there pythaggoras many more Pythagorean triples. For example, based on the 2nd triple on our list 5, 12, 13you know 10, 24, 26 is also a Pythagorean Triple. The conclusion is the sum of the areas of the two smaller squares equals the area of the biggest square, ie. Looking for more LEGO math activities? Save my name, email, and website in this browser for the next time I comment.

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Proof of the Pythagorean Theorem using Algebra

A one-minute video showing you how to prove Pythagoras' theorem: that the area of the square on the longest side of a right-angled triangle is equal to the sum of the squares on the other two sides. For the formal proof, we require four elementary lemmata: If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles included by those sides equal, then the triangles are congruent (side-angle-side). Pythagorean Theorem. Let's build up squares on the sides of a right triangle. Pythagoras' Theorem then claims that the sum of (the areas of) two small squares equals (the area of) the large one. In algebraic terms, a 2 + b 2 = c 2 where c is the hypotenuse while a and b are the sides of the triangle.

Last Updated: October 8, References. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed , times. Learn more The Pythagorean Theorem allows you to work out the length of the third side of a right triangle when the other two are known.

It is named after Pythagoras, a mathematician in ancient Greece. Two common proofs are presented here. Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow.

Download Article Explore this Article methods. Related Articles. Method 1 of Draw four congruent right triangles. Congruent triangles are ones that have three identical sides. Designate the legs of length a and b and hypotenuse of length c. Remember, the Pythagorean Theorem only applies to right triangles.

With the triangles placed in this way, they will form a smaller square in green inside the larger square with four equal sides of length c , the hypotenuse of each triangle. You can rotate turn the entire arrangement by 90 degrees and it will be exactly the same. You can repeat this as many times as you like. This is only possible because the four angles at the corners are equal.

Rearrange the same four triangles such that they form two equal rectangles inside a larger square. The larger of the smaller squares in red has sides of length a , while the smaller square in blue has sides of length b.

Recognize that the area not formed by the triangles is equal in both arrangements. Given this, the areas of both of the large squares are equal. Looking at both arrangements, you can see that the total area of the green square must equal the areas of the red and blue squares added together in the second arrangement. In both arrangements we partially covered the surface with exactly the same amount, four grey triangles that didn't overlap.

This means that also the area left out by the triangles must be equal in both arrangements. Therefore, the area of the blue and the red square taken together must be equal to the area of the green square. Set the areas of each arrangement equal to each other. The blue area is a 2 , the red area, b 2 and the green area, c 2. Method 2 of Simply connect the tops of the left and right sides to complete the trapezoid. Divide the trapezoid into three right triangles, two of which are congruent.

Divide the base of the triangle into lengths a and b so that two right triangles of lengths a , b , and c is formed. The third triangle will have two sides of length c and a hypotenuse of length d. Calculate the area of the trapezoid using the area formula. Find the area by summing the areas of the three triangles. This trapezoid has been broken into three different triangles; therefore, the areas need to be added together. First, find the area of each one and then add all three together.

Set the different area calculations equal to each other. Because both of these calculations are equal to the total area of the trapezoid, you can set them equal to each other. In the example images, how did the red area and blue area equal the green area? That's the trick. If you could, the Pythagorean Theorem would be obvious. If you take away 2ab in the form of two a by b rectangles, you are left with the red and blue squares shown in the left diagram.

If you take away 2ab in the form of four a by b right triangles, you are left with the green square in the diagram on the right. If you start with equal areas, and subtract equal areas, what you are left with must have equal areas. Yes No. Not Helpful 7 Helpful Not Helpful 8 Helpful Is there any other method, preferably involving more of algebra and less of geometry, to prove the Pythagorean Theorem? Not Helpful 1 Helpful 5. Include your email address to get a message when this question is answered.

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