Folding to Construct Shapes: Warmup Problem

1.   If you fold a square piece of paper along one of its diagonals, like this:

     then you get a figure like this:

     What kind of triangle is this?  
     Is it a right triangle?  How do you know?  

     Is it an isosceles triangle?  How do you know?

2.   Where in the non-square rectangle below could you fold in order to locate the center of the rectangle?  Show with dotted lines.  What would you write to    convince someone that you have located the center of the rectangle?  

3.  Show where you would fold Square ABCD in order to create a line segment parallel to segment

Now show where you would fold Square ABCD in order to create a line segment perpendicular to segment

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