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## Geometry (FL B.E.S.T.)

### Course: Geometry (FL B.E.S.T.)>Unit 5

Lesson 1: Theorems concerning triangle properties

# Proofs concerning equilateral triangles

Sal proves that the angles of an equilateral triangle are all congruent (and therefore they all measure 60°), and conversely, that triangles with all congruent angles are equilateral. Created by Sal Khan.

## Want to join the conversation?

• Are the angles in an equilateral triangle always 60 degrees?
• Yes because all triangle angles has to add up to 180 degrees . If the triangle is equalateral then there is 3 angles in an triangle so 180/3 =60
• Why did Sal draw a squiggle on top of the equal sign at ?
• The squiggly line on top of the equal sign means congruent.^_^
• For any triangle, how do you determine what the base is?
Like, if it was tilted on its side, does it really matter which is the base?
• Well, the base could be any one. It doesn't necessarily have to be the one on the bottom
• Are the angles in an equilateral triangle always 60 degrees?
• Yes, because a equilateral triangle has 3 equal angles. The 3 angles of a triangle equal 180°. So if the angles are all equal in an equilateral triangle, we do 60 times 3 which equals 180°.
• If you know it is an equilateral triangle because it is a given, can you not simply postulate that all three angles are congruent as your reasoning?
• Yes, you could. It's obvious. I think mathematicians prove things to this to this crazy level because there have been occasions where our intuition in mathematics is wrong so absolutely everything needs to have a formal basis.

EDIT: I just realised you might be asking what to do if you were asked this under a test condition. In that case, I'd do a reasoning like Sal did here rather than simply using the given equilateral property.
• Is it possible to have equiangular triangle while the length of the triangle aren't congruent? Not equilateral, or isosceles triangle but their length are all different.
• No, because if one leg was longer then the legs would meet at different angles, and therefore, not be equiangular. You could also prove this by using congruency postulates if you sketched out some triangles.
• What is a "base" angle?
• A base angle is any angle in which one of its sides is formed by the triangle's base. Note that base angles can be for any polygon. To find a base angle (a triangle has two base angles), you need to first identify the base. The base angles are the two angles that touch the base.
• i just don't know how to form statements reasons are fine when i am told the statement. how do i learn to make statements
• Do you mean you don't know how to tell which fact to prove next?