Learn the essential concepts of the Pythagorean theorem and when to subtract in problem-solving for young learners.
The Pythagorean theorem is a very important rule in geometry, especially when you are working with right triangles. It states that in a right triangle (a triangle with one angle that is 90 degrees), the sum of the squares of the lengths of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).
The formula looks like this: a² + b² = c², where c is the hypotenuse, and a and b are the legs.
Now, regarding when to subtract while solving problems using the Pythagorean theorem: usually, you don't need to subtract in the calculations of the Pythagorean theorem itself. However, subtraction might come into play when trying to find one of the legs if you are given the hypotenuse and only one leg.
Here's an example to help you understand:
Imagine you have a right triangle where the hypotenuse (c) is 10 units, and one leg (a) is 6 units. To find the length of the other leg (b), you can rearrange the formula:
1. Start with the original formula: a² + b² = c².
2. Substitute in the known values: 6² + b² = 10².
3. Calculate the squares: 36 + b² = 100.
4. To find b², you'll need to subtract 36 from both sides: b² = 100 - 36.
5. So now you have: b² = 64.
6. Finally, take the square root of both sides to find b: b = √64. Therefore, b = 8.
In summary, you generally use subtraction when you need to isolate a variable, usually one of the legs of the triangle, when you need to figure it out from the other measurements. Hope that helps!