# 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.
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.