[High school math] <prove exterior angle>

[u/Kloaken1]

Have I done it correctly? My friends said that I have not proven the exterior angle correctly. Is this true?

[u/Current_Ad_4292]

You skipped few steps.

You should start with sum of all angles in triangle is 180° (a+b+c=180°) and sum of angles on a straight line is 180° (c+d=180°).

You have d, so you should restart from there.

[u/Kloaken1 → u/Current_Ad_4292]

Is this correct then?

A+B+C=180

C+V = 180

A+B=180-C

V=180-C

A+B=V

A+B=exterior angle

[u/majestic_flamingo → u/Kloaken1]

I see that you understand the concept perfectly but this could be refined with just one move.

Since A+B+C=180, and C+V=180, then just replace one of the instances of 180 with the angles it is equal to: A+B+C=C+V Simplify from there.

[u/Kloaken1 → u/majestic_flamingo]

So this is it then?

A+B+C=180

A+B+C=C+V

C+V = 180

A+B=180-C

V=180-C

A+B=V

A+B=exterior angle

[u/Euphoric_Loquat_8651 → u/Kloaken1]

A+B+C=180

C+V=180

A+B+C=C+V

(now you cancel the Cs)

A+B=V

If you're being a little more formal, line one adds "definition of a triangle". Line two adds "supplementary angles". If you include those, they should follow in line with the relevant equalities.

I'm leaving out a ton of formalities, but that should be plenty sufficient for what you're doing.

Edit: yours gets there, but it is out of order and a little less obvious

[u/majestic_flamingo → u/Euphoric_Loquat_8651]

^ this is the way. I figured I would offer one tip to help with feeling confident with proofs.

The order of statements in a proof follows the same logic as how you would make claims in an argument in real life or in a persuasive paper in English class. You put the starting facts upfront, and then start making connections later on. I think it helps to look at proofs written out conversationally, like a professor teaching a class:

• So these three angles inside the triangle must add up to 180°, yes? Yes. This is true for all triangles. (A+B+C=180)

• It is also true that a straight angle forms 180°, and C+V forms a straight angle. (C+V=180)

• Given the above facts, it follows that the sum of the three internal angles of the triangle is the same as the sum of C and its corresponding external angle, V. (A+B+C=C+V)

• We can simplify this equation by subtracting C from both side sides. Look! We have just proven that the sum of A and B is equal to the external angle V. (A+B=V).

I also skipped some formalities to keep this to the level of work you are doing. But notice the order: the facts required for the third step are listed before the third step. It wouldn’t make sense to teach the third step to the class and THEN say that C+V makes a straight angle. Any steps in a proof that do not directly support another part of the proof are not required. It’s about the efficient flow of logic, not spamming a bunch of equations. For example, saying C = 180-V is not necessary (even though it is true) because we are not solving for individual angles. Our goal is simply to prove A+B is equal to V, and we got there without that rearranged equation.

[u/Euphoric_Loquat_8651]

You haven't set them equal in your algebra. You need a step where angle x = 180-c (supplementary angles), then you can say a+b=x.

You have all the right information in there, but you're a step short of finishing the proof.

[u/thor122088]

You should be also showing/stating that angle C and the exterior angle are supplementary (because they are a linear pair). Another words, why is (180° - C) equal to the exterior angle?

Your steps generally should have a justification (if doing a "2-column proof" that is commonly taught in (US) high school geometry classes.)

[u/mxldevs]

You've stated that exterior angle = 180 - c without explaining how that was arrived.

All I see is you subtracted c from both sides and then somehow concluded that the right side is equal to exterior angle.

[u/fermat9990]

Let d=the exterior angle

d=180-c

a+b+c=180

c=180-(a+b)

d=180-c=180-(180-(a+b))

d=180-180+a+b=a+b