Analysis of the proof process of triangle inner angles and theorem

Mondo Education Updated on 2024-01-28

Three minutes to talk about popular science

Hello everyone!Today we are going to take a very interesting mathematical problem, that is, how to prove that the sum of the internal angles of any triangle is equal to 180 degrees. Everyone learned this theorem in junior high school, but the process of proving it is very interesting, so let's take a look!

Figure 1 is a triangle with A being the vertex and BC being the bottom edge. So why do we need to make a straight line L through the point a, because the properties of parallel lines and the definition of flat angles can help us prove that the sum of the internal angles of a triangle is equal to 180.

We can draw Figure 1, in addition to the triangle abc, and don't forget to draw the straight line l, and then cut out b and c. You will find that a, b, and c can form flat angles.

The following is the most classic method of proving geometry, which is also the core content of the triangle inner angle and theorem.

Known: ABC (Figure 1).

Verification: A + B + C = 180

Proof: As shown in Figure 1, the point A is used as a straight line L, so that L BC

l bc, 2 = 4 (two straight lines are parallel, and the inner wrong angles are equal).

Similarly 3 = 5

1, 4, 5 make up a flat angle, 1 + 4 + 5 = 180 (flat angle definition).

1 + 2 + 3 = 180 (equal substitution).

Above we have proved that the sum of the internal angles of any triangle is equal to 180, and we get the following theorem, the sum of the internal angles of the triangle: the sum of the three internal angles of the triangle is equal to 180

This theorem can be said to be one of the most classic theorems in geometry, and it is also a theorem that we often use in our Xi and life. Through this theorem, we can solve many practical problems, such as calculating angles, proving equality relations, and so on.

In conclusion, triangle inner angles and theorems are a very useful mathematical tool that not only helps us solve practical problems, but also allows us to better understand some concepts and properties in geometry. If you haven't mastered this theorem yet, you might as well go and Xi it now, I believe you will benefit a lot!

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