Quadrilaterals

R-53 What do we know about triangles?

-Exterior + interior
-Angle sum =180 degrees
*at least 3 pieces of info needed for duplicating a triangle
-They can tile and tessellate 
*2 small sides greater>biggest side

Quadrilaterals -How many pieces of information do we think we would need to give? 
-4 pieces of information needed (3 angles, 1 side or 4 sides)
-2 for some where2 sides are the same (if equilateral)
-3 (side, side, angle)
*Class still is not sure how many pieces of info. would be needed

Side Lengths            Did we create a unique quad?                    Sketch
6,10,15,15                yes-unique-only one can be made
3,5,10,20                  no-not unique-multiple quads can be made
8,8,10,10                  Impossible-can't make a quad
12,20,6,9

Make up your own

L-53 Make 5 observations about your chart
-No unique quads
-were repeated #'s in side lengths
-may need < to make unique(conjecture)
-both angles and side lengths are relevant for unique shapes
-these smallest +2 >largest to make quadrilateral (because of extra bend in the shape)
-All could shift around to make lots of quads

Students were given a challenge. They needed to make a quadrilateral. Then, needed to make a structure so that it would be stable and not move because there are no unique triangles.

Chris discovered that if you put a poly strip in the middle it creates two triangles. Triangles are unique.

Creating triangles creates stability.

Many builders create triangles. There are many structures that have triangles throughout.

L-53 2 Big Ideas:
 1st Big Ideas
You can't make a unique quadrilateral because it is flexible.
To make a quad stable, create 2 triangles with a diagonal


2nd Big Idea:
Their side lengths have to be bigger than the biggest one.
Their smallest +2 >largest to make quad