Chapter 5: Properties of Polygons

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Chapter 5: Properties of Polygons
Objective: Discover relationships among the sides, angles, and diagonals of polygons Study the properties of polygons Use polygons to solve problems

Polygon terms we know: Polygons Descriptors or parts Pentagon
Quadrilateral Pentagon Concave Trapezoid Convex Hexagon Kite Octogon Rectangle Vertex Side Square Diagonal Regular Polygon

Polygon Sum Conjecture
Objective: Write a conjectures about the sum of the angle measures of a polygon

1. Draw 2 of your assigned polygon.
2. Measure and label all interior angles. 3. Find the sum of all interior angles. 4. Compare your results with person sitting next to you. The sum of the measures of the n interior angles of an n-gon is ______________. Polygon Sum Conjecture 1800 (n – 2) ? . . . Sum of interior angles n 8 7 6 5 4 3 # of sides of polygon 1800 3600 5400 7200 9000 10800 1800 + 1800 + 1800 + 1800 180(3) + ______= 180 180(3) + 180(-2) = 180 180 (3 – 2) = 180 -360 ( – 2) n nth term:

a + b + c = 1800 x + y + z = 1800 x a Triangle Sum Conjecture y (a + b + c) + (x + y + z) = 3600 b Addition Property of equality Sum of the measures of the interior angles of a quadrilateral equals 3600 c z Pg 257 #1-14, 16

Count the triangles you made it is clear to see,
Take a point on your poly as a place to start. Draw the lines to the corners, a work of art. (The poly, the poly, the poly formula) Count the triangles you made it is clear to see, there are 2 less than sides or vertices. (The poly, the poly, the poly formula) 180 is the count of each triangle you draw Add them all together for the total sum law (The poly, the poly, the poly formula)

There is more to the story than what’s inside
The sum of all angles for a polygon you do is the product of 180 and (n - 2) There is more to the story than what’s inside For the outside use 360 as your guide Inside and outside a linear pair all sides the same makes it regular. There’s a special rule for the exterior: Sides and angles are the same: it is regular

Inside and outside a linear pair all sides the same makes it regular
360 divided by sides gives each angle 360 divided by angles gives each side Inside and outside a linear pair all sides the same makes it regular The next thing to do is to find a side When the angle just happens to be inside. Subtract it form 180 (it’s a linear pair) Use the rule above now its exterior!

The last thing to do is a quick review
Study, do you classwork, its up to you! The sum of all angles for a polygon you do is the product of 180 and (n - 2) The product of 180(n – 2) There’s a special rule for the exterior: 360 divided by sides gives each angle 360 divided by angles gives each side Inside and outside a linear pair all sides the same makes it regular.