induction q. from fitz. (2 Viewers)

[~*HSC 4 life*~]

dude, don't be ashamed to ask q's! and i'm sure Cm tutor and others are happy to help you out! i would if i could

 

[dilos]

thanks heaps, it's so reassuring to have you guys help out!!

*hugs the maths ext1 forum*

 

[dilos]

Originally posted by CM_Tutor
This question was discussed on the other current induction thread - have a look, and then try it yourself.

And no, I'm not annoyed. Why do you ask?

i'm feeling really bad for asking so many q's...as long as it's ok, thanks so much- i really really appreciate it.

 

[dilos]

i got stuck half way through this!! what do you do!!!

Prove by induction:

The sum of the angles of a polygon of n sides is (2n-4)right angles, n=>3

 

[CM_Tutor]

Originally posted by dilos
i got stuck half way through this!! what do you do!!!

Prove by induction:

The sum of the angles of a polygon of n sides is (2n-4)right angles, n=>3

First part is straight forward - you just have to prove that the angle sum of a triangle is 180.

For the second part, you've assumed the result for a k-sided polygon(a 'k-gon'), and must prove it for a
(k + 1)-gon. To do this, label the vertices of your (k + 1)-gon sequentially as V₁, V₂, V₃, ..., V_k+1. Now, join V₁ to V₃. The angle sum of the (k + 1)-gon is equal to the angle sum of the triangle V₁V₂V₃ (which you know is 180 from the first part) plus the angle sum of the k-gon V₁V₃V₄...V_k+1 (which you know from the induction hypothesis). The solution should follow from there. Clear?