Can every quadrilateral be divided to 2 triangles?0
polygon of 4 sides.What is the definition of a quadrilateral - according to your textbook?
There aren't really only two examples. Either you can simply connect any two opposing points, or you can only connect one set of opposing points.Can every quadrilateral be divided to 2 triangles?
Yes.Can every quadrilateral be divided to 2 triangles?
This would be a far more interesting discussion if you would tell us your own thoughts. Did you have a reason to think the answer is yes? Did you have a reason to be unsure of your answer? Did you try a number of different quadrilaterals, including both convex and concave? All of that is worth talking about.Can every quadrilateral be divided to 2 triangles?
Are you saying that your question is based on a problem you found somewhere that mentions convex and concave? Please show us the problem!Yes the solutions is looking about convex polygon and concave polygon.
Why would you believe them? The article is about an entirely different problem (and far larger). I see no mention of triangles.1. There is the article I was referred to:
Someone tell me that this article show why it is true.
What are "all the cases"? There are an infinite number of quadrilaterals.2. My thoughts is using elimination to show all the cases one-by-one, to show all the possibilities that it true.
I can't read the article.Yes the solutions is looking about convex polygon and concave polygon.
1. There is the article I was referred to:
Someone tell me that this article show why it is true.
2. My thoughts is using elimination to show all the cases one-by-one, to show all the possiblites that it true.
Please draw pictures of a convex quadrilateral and a concave quadrilateral, and think about whether your reasoning is true in every case (regardless of the starting vertex).I think about using the fact that the sum of the angles in triagnle is 180 degrees.
When we pass a line to the opposite vertex we divided the area to 2. The angles that created is external angle that influence on the other angles in the other triangle.
Because the quadriletral is a polygon that compose from 360 degrees there can't be any sum that greater from 360 degrees.
So, I think by showing that the figure is a polygon with 180 degrees can define as triangles.
By using the property that the have excatly 180 degrees, I prove that the figures that created is 2 triangles.
I think my proof is for convex quadriletral
If we just want a direct answer to the question itself (is it true?), it's already been said repeatedly that the answer is yes. Yes, that's a simple question.I don't understand how this has become so complicated!
The question in the file I get was truncated.lIf we just want a direct answer to the question itself (is it true?), it's already been said repeatedly that the answer is yes. Yes, that's a simple question.
I then opened it up to the bigger question, to make it interesting: How do we know it's true, and why did @shahar have to ask it? That makes it just a little more complicated, because now we are talking about how to think, not just what to think, and there are different ways to think. My suggestion is that just drawing two pictures may be enough; but more may be wanted, and even that hasn't been done yet.
I assume you know how to divide each of these into two triangles?Here the file.
Happy New Year.
Yes.I assume you know how to divide each of these into two triangles?