Math Is Fun Forum

jadewest

Member

Registered: 2021-02-20

Posts: 44

Proofs

Hello!!

I have completed a lesson about proofs. I am unsure about two questions I've answered.

3. I have drawn a polygon with eight sides, so it must be an octagon.

A. Definition of supplementary angles
B. unfounded
C. Definition of radius
D. 1267200 inches
E. Definition of an octagon
F. Given

    For this one I have selected alternative E, definition of an octagon, because it defines what an octagon is.

4. A square has two diagonals.

A. Given
B. unfounded
C. Definition of an octagon
D. The number of diagonals is (n-3)n/2, where n is the number of sides, which is 4 for a square.
E. 1267200 inches
F. Definition of supplementary angles

     For this one I have chosen alternative A, given, because a square has 2 diagonals and that is the exact thing that the statement is saying.

Am I correct in these two?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Proofs

hi jadewest

Q3.  E looks right to me.

Q4.  A square is a type of quadrilateral, ie n = 4.  So you can calculate how many diagonals it has using the formula specified in D

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jadewest

Member

Registered: 2021-02-20

Posts: 44

Re: Proofs

Hi Bob,

What is confusing me right now is that from the formula in D it turns out to be 2 diagonals.
(4-3)* 4/2=
= 1*2
=2 diagonals

   The statement says that it has 2 diagonals. Given is when the statement is given, it means that it is provided to me in the problem. That is why I was going for given in this exercise.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Proofs

This exercise is confusing me too.  Here's the way I see it.  We're told that it's a square.  Having two diagonals is not a defining property for a square as many other polygons have two diagonals as well.

So if you were told a polygon had two diagonals you couldn't conclude it was a square.  So the statement "A square has two diagonals" is not a given statement, it is a consequence of a property of polygons which is they always have (n-3)n/2 diagonals.  So the statement is the result of the formula not a defining property for squares.

Is this a Compu-High worksheet?  I've had my brain twisted by their attempts to teach proofs before.  Luckily in the UK such things are not in the curriculum; proving things yes, but not trying to get your head around the difference between something being given and something being proved.  To argue my case fully , I'd have to go back to how squares have been defined in your course.

Sorry this isn't a definitive answer; you'll just have to take a risk with which answer you like best.

Good luck,

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob