Sum Of All Angles of a Triangle is 180 degrees (proof)

In this lesson we will give proof that the sum of the interior angles of a triangle is 180 degrees. This proof is necessary because from the knowledge that the sum of all angles in a triangle is 180 degrees, we can then use triangles and their angle measurements to calculate all other types of polygons, whether they be squares, quadrilaterals, Pentagons etc.

What you need to know to understand this proof:

To understand this proof there are two things you need to know.

1)t ‘the sum of all angles on a straight line is 180 degrees’, and
2) You also need to know how to find alternate angles

If you are unsure about how to find alternate angles, here is a link to my video on the subject where I discuss the basics of both Corresponding angles, AND alternate angles:
   • How To Find Corresponding And Alternate An...  

Feel free to check that video out after you have watched today’s lesson on how we prove that the sum of all angles in a triangle is 180 degrees.

Once we have shown the proof we will then look at a few examples of how you can use triangles to determine the sum of all angles in other polygons such as Pentagons and Hexagons and even oddly shaped polygons.

For a full understanding of why the triangle angles of 180 degrees is so important, I also recommend watching my video on why the formula (n-2)180° works for finding the sum of angles in ANY polygon and how the sum of angles in a triangle is related to this formula. Here’s the link to that video:
   • Finding Angles in A POLYGON: why (n-2)*180° ?  


Feel free to follow on to that video after today’s lesson.

Contents:

0:00 - Introduction - What You’ll learn (The sum of all angles of a triangle is 180 - Proof)
0:18 - Knowledge You Need Beforehand
1:02 - Preparing the Triangle Layout for the Proof
3:00 - Finding Alternate Angles Of The Triangle’s Inner Angles
4:11 - Showing the Alternate Angles and one inner angle = 180 degrees
5:15 - Finishing up; A + B + C, Sum of angles of a triangle is 180 degrees
5:45 - Using Triangles’ sum of 180 degrees to measure other Polygons
7:00 - Summing up and other useful videos


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