Question

What are the first 15 steps to show triangle ABC with measurement angle ABC equals 90°? The first 10 steps prove a² +b²=c² .

Answer 1

The question pertains to demonstrating the Pythagorean theorem in a right triangle with a 90-degree angle at vertex B. This is done by identifying the legs and the hypotenuse, squaring the lengths of the legs, adding them, and equating them to the square of the hypotenuse.

Step-by-step explanation:

The question revolves around proving that in triangle ABC, with angle ABC measuring 90°, the Pythagorean theorem a² + b² = c² holds true, where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse of the right triangle. To demonstrate this, we assume that angle ABC is the right angle and follow these steps:

1. Understand that the Pythagorean theorem applies to right triangles.
2. Identify the legs a and b of the right triangle ABC.
3. Recognize that the side opposite the right angle, the hypotenuse, is labeled c.
4. Using the theorem, set up the equation a² + b² = c².
5. If necessary, measure or find the lengths a and b.
6. Square both lengths a and b to get a² and b² respectively.
7. Add the squared lengths together.
8. Understand that this sum equals the square of the hypotenuse c².
9. If you need to find the length of the hypotenuse, take the square root of the sum of squares of a and b.
10. Verify that this process correctly gives the length c when squared.
11. Check your result by confirming that a² + b² indeed equals c².
12. Reinforce that this relationship operates solely in right triangles.
13. Recognize the arrangement of the triangle legs and the hypotenuse in the Cartesian plane if coordinates are involved.
14. Utilize the equation to solve practical problems involving right triangles.
15. Lastly, comprehend that this triangle ABC is a model of the consistency of the Pythagorean theorem.