1.5: Polygons. =convex and concave. p. 514-521. GSE’s. Primary.
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=convex and concave
M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).
Convex polygon: if you extend any side of the polygon, you will not go through the figure
Concave polygon: the opposite is true (it caves in)
+ + = 180
mA + mW+ mE=180o
(3x+5) + ( 8x+22) + (4x-12) = 180
15x + 15 = 180
15x = 165
x = 11
mA = 3(11) +5 = 38o
8x + 22
mW = 8(11)+22 = 110o
4x - 12
mE = 4(11)-12 = 32o
Triangle AWE is obtuse
1) Pick any vertex.
2) Make a darker point at it.
3) Connect that point to every other vertice in the polygon
Write down how many non-overlapping triangles are formed.
Extend any one side of the figure
The angle formed is the
exterior angle. It’s a linear pair
With the inside angle
HANDOUT on investigating polygons angles
Convex Polygon Number of Number of Sum of interior Sum of ext.
sides ‘s Angles Angles
The formula for finding the sum of the interior angles of any convex polygon is :
What is an example of a regular 4 sided polygon?
How about a 3 sided polygons?
Find the measure of angle N
of a regular polygon is 160. How many
sides does the regular polygon have?