Pythagorean theorem is really simple. You will learn functions later, and you will find them. The key is to use the theorem A 2+B 2 = C 2 flexibly.
The problem is not that it is difficult, but that it has many test sites. If we can break them one by one, the difficulty will be solved.
I believe you will find that when you solve a problem, just set the formula directly.
The general exam is like this,
Given that ∠ c = 90, BC=5 and AC= 12 in △ABC, find the value of AB.
It's simple. You can directly find out according to Pythagorean theorem:
The opposite side of c is AB, so AB is the hypotenuse.
∠△ABC，∠ c = 90。
∴AB^2=BC^2+AC^2
∴AB= 13
In addition, the Pythagorean theorem test will be used to determine the right triangle. You must remember,
People ask you:
A triangle satisfies A 2+B 2 = C 2. What triangle is it?
You can find the inverse theorem of Pythagorean theorem: right triangle.
I can also give a variant question:
Three sides of a triangle satisfy
(A-3) 2+(B-4) 2+(C-5) 2 = 0。 What triangle is this?
It is easy to work out that this is a right triangle.
There is also the concept of Pythagoras number. As long as a positive integer satisfying A 2+B 2 = C 2 is a pythagorean number, note that it is a positive integer. If they are zero numbers, although they can form a right triangle, they are not pythagorean numbers.
It is skillful to judge the number of Pythagoras. For example, if someone asks you whether 15,20,25 is a Pythagorean number, you can calculate it skillfully:15 = 5 * 3,20 = 5 * 4,25 = 5 * 5, ∫ 3,4,5 is a Pythagorean number, so 654 is a Pythagorean number.
There are also classified discussions.
People ask you, in a right triangle, one side is 12 and the other side is 5, so find the third side.
This involves the idea of classified discussion.
Ordinary students will definitely find that the third side is 13, but after careful calculation, it is not difficult to find another solution. If 12 is regarded as a hypotenuse and 5 as a right angle, then the third side = root number 1 19.
The teacher summed up all kinds of problems for you, did you understand?