geometry proofs by induction (1 Viewer)

[BIRUNI]

can anyone please explain how we prove geometry results by induction?

I have seen the solution for this question but i do not understand it.
question: prove by induction that the sum of exterior angles of a n-sided polygon is 360.

 

[Affinity]

You should think of induction as proving something by dividing the statement into cases: (first case, second case, third case, fourth case, so on).

So here, it will be natural to set this to the number of sides: ie 'n' in your induction is the number of sides of the polygons.

So first you prove the base case that when n=3, it works (ie, a triangle's exterior angles add up to 360)

Then you try to prove that the exterior angle some of a (n+1)-gon is 360 if it is so for any n-gon. (this might take some work if you allow concave polygons)

then by induction it works.

 

[zeek]

I think the geometry proofs are often reserved for things dealing with angles or straight lines intercepting each other. To be honest i haven't seen many

for this question, you'd do something like this...

S(3):
For a 3-sided polygon (triangle, with angles A,B,C), the exterior angles are equal to the opposite internal angles. Therefore, the sum of these exterior angles = 2(A + B + C). We know that the sum of the interior angles of a triangle = 180^o .: Sum exterior angles = 2.180
= 360

S(k):
Assume for some k-sided polygon that the sum of exterior angles is 360.

S(k+1):
Working from S(3), if S(k+1) is some 4 sided polygon (rectangle), then it can be shown geometrically that the sum of its exterior angles is 360.

.: By M.I blah blah blah