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## Class 10 (Foundation)

### Unit 9: Lesson 3

Proof of triangle properties

# Angles in a triangle sum to 180° proof

Learn the formal proof that shows the measures of interior angles of a triangle sum to 180°. Created by Sal Khan.

## Want to join the conversation?

• What is the sum of the exterior angles of a triangle?
• The sum of the exterior angles of any shape is 360 degrees
• At , Sal mentions that he has "drawn an arbitrary triangle." What is an arbitrary triangle?
• Arbitary just means random. Sal means he just drew a random triangle with sides of random length.
• If the angles of a triangle add up to 180 degrees, what about quadrilaterals? Are there any rules for these shapes? ( e.g. do all of the angles in a quadrilateral add up to a certain amount of degrees?) If there is a video on Khanacademy, please give me a link.
• Consider a square. All the sides are equal, as are all the angles. A square has four 90 degree angles. 90 x 4 = 360.

• Is there a more simple way to understand this because I am not fully under standing it other than just that they add up?
• Try finding a book about it at your local library. They may have books in the Juvenile section that simplifies the concept down to what you can understand. This normally helps me when I don't get it!
• what is a median and altitude in a triangle
• A median in a triangle is a line segment that connects any vertex of the triangle to the midpoint of the opposite side. An altitude in a triangle is a line segment starting at any vertex and is perpendicular to the opposite side.
• At , Sal states that we are using our knowledge of transversals of parallel lines. What does that mean?
• if the sum of the angles are more than 180degrees what does the shape be
• The proof shown in the video only works for the internal angles of triangles. With any other shape, you can get much higher values. Take a square for example. Squares have 4 angles of 90 degrees. That's 360 degrees - definitely more than 180.
A regular pentagon (5-sided polygon) has 5 angles of 108 degrees each, for a grand total of 540 degrees. That's more than a full turn.
But why stop there? A regular 180-gon has 180 angles of 178 degrees each, totaling 32040 degrees. You can keep going like this forever, there is no bound on the sum of the internal angles of a shape. And this is not only true for regular polygons. Just draw any shape with more than 3 sides, and the internal angles will sum to more than 180 degrees.
• Im in 7th grade. When i started it was hard I think the way I learned from my teacher is harder because I cant ask the teacher to repeat it or pause soi can write the problem down but when he assigned me this while the highschoolers had a field trip. khan academy's is WAYYYYYYYYYYYYYYYYYYy....WAY*100 easier and more fun.