Tuesday September 13
Geometric Puzzle Foundations
 Measuring angles, lengths and areas.
 Squares, rectangles : 90 degree/ right
angle
 parallelograms: opposite angles are congruent,
sum of consecutive angles =180 degrees
 triangles
: add to 180 degrees straight angle [Illustrated physically and with wingeometry]
 Dissections, cut and paste methods of measurement.
 Cutting and reassembling polygons.
 The
"Square Me" Puzzle
 The triangle, quadrilateral, pentagon, and hexagon.
 More on measurements of angles and areas of polygons.
 A quadrilateral can be made from two triangles...
so the sum of its interior angles is 2 * 180 = 360.
 A pentagon can be made from 3 triangles...
so the sum of its interior angles is 3* 180 = 540. If the pentagon has
all angles congruent( of equal measurement) then each angle will be 540/5
= 108 degrees!
 A hexagon can be made from 4 triangles...
so the sum of its interior angles is 4* 180 = 720. If the hexagon has all
angles congruent( of equal measurement) then each angle will be 720/6 =
120 degrees!
# of sides

# of Triangles

Sum of Interior <‘s

If equal, Measure of a single <

3

1

180

60

4

2

360

90

5

3

540

108

6

4

720

120

N

?



Puzzles and Polygons
 Dissections, cut and paste methods of measurement.
 Cutting and reassembling polygons.
Tangoes: a commercial game based on tangrams
Cutting and reassembling polygons.
Convex: Any two points in the figure
have a line segment connecting them. If that line segment is always inside the figure, then the figure
is called "convex".
Making Dissection Puzzles:
Dissection of the plane Tilings
of the plane:
Tessellations
 Activity: Tile plane with playing cards.
 Discuss briefly: Symmetry of playing cards
 reflection (vertical line/ horizontal
line)
 180 deegree rotation
 Preview ... Possible tiles and tilings.
 One Regular Convex Polygon.
 Two or more Regular Convex Polygons.
 Other Polygon Tilings.
 Non polygonal tilings.