The Pythagorean Theorem is a very useful math rule that helps us find the length of a missing side of a right triangle. Let's understand it using a cool image!
Look at this picture. It shows a square shape divided into four smaller right triangles. Each of these triangles has a right angle (90 degrees) and two shorter sides. One side is horizontal, and the other is vertical.
Take a close look at the triangles. Notice that the shortest side of a triangle is actually a part of the square's side. And the longest side of a triangle is the diagonal of the square.
Now, let's examine the relationship between the sides of the triangle. According to the Pythagorean Theorem, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides (the legs).
For example, if the shortest side (one leg) has a length of 3 units, and the other leg is 4 units, we can use the Pythagorean Theorem to find the hypotenuse. We square the lengths of both legs: 3^2 = 9 and 4^2 = 16. Then, we add those two results together: 9 + 16 = 25.
Now, we need to find the square root of 25 to get the hypotenuse's length. The square root of 25 is 5.
So, using the Pythagorean Theorem, we found that the hypotenuse (the longest side) of this triangle is 5 units. This rule works every time for any right triangle!
It's like magic! We can find any missing side of a right triangle by using the Pythagorean Theorem. Just remember the formula: a² + b² = c², where 'a' and 'b' are the two legs, and 'c' is the hypotenuse.
Explain a proof of the Pythagorean Theorem using the image. The image is the image of four right triangles and a square proof of the Pythagorean Theorem.
make it how a 7th grader would write it.
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shorter pls
Sure!
The Pythagorean Theorem says that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the picture, we see a square divided into four smaller right triangles. Each triangle has one side that is part of the square's side, and another side that is part of the square's diagonal.
If we know the lengths of the two shorter sides of a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse.
For example, if one side is 3 units long and the other side is 4 units long, we square both lengths: 3² = 9 and 4² = 16. Then, we add those two results: 9 + 16 = 25.
To find the length of the hypotenuse, we need to take the square root of 25, which is 5.
So, using the Pythagorean Theorem, we found that the hypotenuse of this triangle is 5 units. This rule helps us find missing sides of right triangles. It's like magic! Remember the formula: a² + b² = c², where a and b are the two shorter sides, and c is the hypotenuse.
The Pythagorean Theorem says that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the picture, we see a square divided into four smaller right triangles. Each triangle has one side that is part of the square's side, and another side that is part of the square's diagonal.
If we know the lengths of the two shorter sides of a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse.
For example, if one side is 3 units long and the other side is 4 units long, we square both lengths: 3² = 9 and 4² = 16. Then, we add those two results: 9 + 16 = 25.
To find the length of the hypotenuse, we need to take the square root of 25, which is 5.
So, using the Pythagorean Theorem, we found that the hypotenuse of this triangle is 5 units. This rule helps us find missing sides of right triangles. It's like magic! Remember the formula: a² + b² = c², where a and b are the two shorter sides, and c is the hypotenuse.
sumerize this
1 answer