Download Geometry: From Triangles to Quadrilaterals and Polygons .

Geometry: From Triangles to
Quadrilaterals and Polygons
MA.912.G.2.1 Identify and describe convex,
concave, regular, and irregular polygons.
Block 22
Polygon
Definition:A closed plane figure, having at least
three side that are line segments and are
connected at their endpoints
• Sides of polygons are sides or edges,
endpoints of sides are vertexes or corners
Polygon
• Examples of polygons:
triangles, quadrilaterals,
pentagons, hexagons
etc.
• Polygons play important
role in Euclidean
geometry, we can also
see them in nature,
science and everyday
life
Examples of polygon
• Search the internet for other polygons:
• Irregular triangles like isoscales triangles, right
angle triangles
• Quadrilaterals like rectangles, parallelograms,
trapezoids
• Other irregular polygons: is a star a polygon?
More definitions for polygons
Convex polygon: Defines a shape that curves
outward; opposite of concave. A geometric
figure is convex if every line segment
connecting interior points is entirely contained
within the figure's interior
Concave polygon: Defines a shape that curves
inward; opposite of convex.
Convex and concave polygons
Regular polygons
• A regular polygon is a polygon which is
equiangular (all angles are equal in measure)
and equilateral (all sides have the same
length)
Examples of regular polygons:
• Name the regular polygons below:
• What are the angles of regular polygons?
Naming
polygons:
Calculating interior angles for
regular polygons:
• To calculate interior angle for a polygon we
divide a regular polygon into triangles drawing
diagonals from one vertex to all others
• Each triangle has sum of angles 1800
Calculating interior angles for
regular polygons:
• To find an angle we multiply the number of
triangles by angles 1800 and divide by the
number of vertexes: for the pentagon that will
be: (3* 1800 )/5=(540)/5=108
Calculating interior angles for
regular polygons:
Polygons and coordinate system
• Question: if the three vertexes of a square are:
A=(2,1), B=(1,3), C=(3,4)
• What are the coordinates of forth vertex?
What is the length of a side of this square?
Solution: the picture below
illustrates the situation
Solution: the picture below
illustrates the situation
•
•
•
•
Answer:
Fourth vertex
D=(4,2)
Side length:
(1  2) 2  (3  1) 2 
(1) 2  (2) 2 
5
Challenge with polygons
• Can we cut an equilateral triangle into four
pieces that can be rearranged to make a
square?
• The Haberdasher's Puzzle, the greatest
mathematical discovery of Henry Dudeney,
was first published by him in the Weekly
Dispatch in 1902 and then as problem no. 26
in The Canterbury Puzzles (1907)
Haberdasher's puzzle
Designing a Table Both Swinging and Stable
Greg N. Frederickson
Review and Discussion
Basing on the lecture on reading:
Designing a Table Both Swinging and Stable by
Greg N. Frederickson
How use the recourses form the module in a
classroom setting?