Homework 2

Hey everyone! After thinking about ideas about proofs, I really liked David's use of shapes to prove the Pythagorean Theorem.

My idea of an interesting proof would be:

How can the area of a Parallelogram be the same formula to find the area of a square or rectangle when a parallelogram does not contain 4 right angles within the shape?

I would like to take the concept of breaking down a parallelogram into shapes and angles and look at the properties all quadrilaterals share.

If we draw lines from one corner to it's opposing corner (creating a cross of the lines in the centre of each shape, we will find that we have 2 obtuse angles and 2 acute angles within the centre of the parallelogram, but we have four 90 degree angles within the square. We also have 4 triangles inside each quadrilateral. Note we also have 2 sets of parallel lines in each quadrilateral (top and bottom, sides). We can summarize all of this by saying we have 2 visually different shapes but how do be prove that Area=base*height for both the parallelogram and the square?

We can discuss the laws of opposing angles combined with the properties of a quadrilateral.

Any thoughts?

Hey Paige, sorry for the late reply, only saw this just then. I quite like this idea. Is there anything you would like me to do/add/research on? or mainly just your question of, "how do be prove that Area=base*height for both the parallelogram and the square?"

Hey, so yeah it needs to be on paper in some decent form of a project. not sure what you want to do with it? I only posted this like an hour ago or so, so no worries.

I will list properties of quadrilaterals and how 2 different shapes can become the same shape? if you want to write a list of maybe 4 or 5 questions we could 'ponder' about in this proof. and lets each come up with a proof so we have some material to compile in the morning and hand in. you can text me at 604.202.7843 if you want to discuss it that way.