6.1 Polygons. Geometry Mrs. Spitz Spring 2005. Objectives:. Identify, name, and describe polygons such as the building shapes in Example 2. Use the sum of the measures of the interior angles of a quadrilateral. Assignments. pp. 325-327 # 4-46 all Definitions Postulates/Theorems.
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Not D – has a side that isn’t a segment – it’s an arc.
Not E– because two of the sides intersect only one other side.
Not F because some of its sides intersect more than two sides/Example 1: Identifying Polygons
Figures A, B, and C are polygons.
Concave or non-convex if a line does contain a side of the polygon containing a point on the interior of the polygon.Convex or concave?
See how it doesn’t go on the
See how this crosses
a point on the inside?
A polygon is EQUILATERAL
If all of its sides are congruent.
A polygon is EQUIANGULAR
if all of its interior angles are congruent.
A polygon is REGULAR if it is
equilateral and equiangular.
Decide whether the following polygons are regular.Identifying Regular Polygons
Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon.
Pentagon is equilateral and equiangular, so it is a regular polygon.
Equilateral, but not equiangular, so it is NOT a regular polygon.
m1 + m2 + m3 + m4 = 360°
3x + 150 = 360
3x = 210
x = 70
Sum of the measures of int. s of a quadrilateral is 360°
Combine like terms
Subtract 150 from each side.
Divide each side by 3.
80°Ex. 4: Interior Angles of a Quadrilateral
Find m Q and mR.
mQ = x° = 70°
mR = 2x°= 140°
►So, mQ = 70° and mR = 140°