Polygons in Geometry
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3-4 THE POLYGON
3-4 THE POLYGON
ANGLE-SUM THEOREM
ANGLE-SUM THEOREM
GEOMETRY
GEOMETRY
Polygon:
Polygon:
a
a
closed
closed
plane figure with at least three
plane figure with at least three
sides
sides
. The sides
. The sides
intersect only at their endpoints, and no adjacent sides are
intersect only at their endpoints, and no adjacent sides are
collinear
collinear
Ex. 1)
Ex. 1)
Name the polygon and identify the vertices,
Name the polygon and identify the vertices,
sides, and angles.
sides, and angles.
Classify a Polygon - Sides
Classify a Polygon - Sides
■
A
A
convex polygon
convex polygon
has no diagonal with points
has no diagonal with points
outside the polygon.
outside the polygon.
Classify a Polygon - Shape
Classify a Polygon - Shape
■
A
A
concave polygon
concave polygon
has at least one diagonal with
has at least one diagonal with
points outside the polygon.
points outside the polygon.
Classify a Polygon - Shape
Classify a Polygon - Shape
Ex. 2) Classify each polygon by its sides. Identify
Ex. 2) Classify each polygon by its sides. Identify
each as either convex or concave.
each as either convex or concave.
Polygon Angle-Sum Theorem
Polygon Angle-Sum Theorem
Ex. 3) FIND THE SUM OF THE MEASURES OF THE
Ex. 3) FIND THE SUM OF THE MEASURES OF THE
GIVEN POLYGON.
GIVEN POLYGON.
■
The sum of the measures of the exterior angles of a
The sum of the measures of the exterior angles of a
polygon, one at each vertex, is 360.
polygon, one at each vertex, is 360.
Polygon Exterior Angle-Sum Theorem
Polygon Exterior Angle-Sum Theorem
■
Equilateral Polygon
Equilateral Polygon
– all sides congruent.
– all sides congruent.
■
Equiangular Polygon
Equiangular Polygon
– all angles congruent
– all angles congruent
■
Regular Polygon
Regular Polygon
– both equilateral and equiangular.
– both equilateral and equiangular.
Vocabulary
Vocabulary
Ex. 5
Ex. 5
)
)
Find the measure of an interior angle
Find the measure of an interior angle
and an exterior angle of each REGULAR
and an exterior angle of each REGULAR
polygon.
polygon.
Explore the concept of polygons, their sides, vertices, and angles, and learn to classify them as convex or concave. Discover the Polygon Angle Sum Theorem and find the sum of measures of angles in a given polygon.
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Presentation Transcript
3 3- -4 THE POLYGON 4 THE POLYGON ANGLE ANGLE- -SUM THEOREM SUM THEOREM GEOMETRY GEOMETRY
Polygon: Polygon: a a closed closed plane figure with at least three plane figure with at least three sides intersect only at their endpoints, and no adjacent sides are intersect only at their endpoints, and no adjacent sides are collinear collinear sides. The sides . The sides
Ex. 1) Ex. 1) Name the polygon and identify the vertices, Name the polygon and identify the vertices, sides, and angles. sides, and angles.
Classify a Polygon Classify a Polygon - - Sides Sides SIDES SIDES 3 4 5 6 8 9 10 12 n Name Name Triangle Quadrilateral Pentagon Hexagon Octagon Nonagon Decagon Dodecagon n-gon
Classify a Polygon Classify a Polygon - - Shape Shape A convex polygon convex polygon has no diagonal with points outside the polygon.
Classify a Polygon Classify a Polygon - - Shape Shape A concave polygon concave polygon has at least one diagonal with points outside the polygon.
Ex. 2) Classify each polygon by its sides. Identify Ex. 2) Classify each polygon by its sides. Identify each as either convex or concave. each as either convex or concave.
Polygon Angle Polygon Angle- -Sum Theorem Sum Theorem The sum of the measures of the angles of an n-gon is: ??? = ? 2 180 ? = ?????? ?? ?????
Ex. 3) FIND THE SUM OF THE MEASURES OF THE Ex. 3) FIND THE SUM OF THE MEASURES OF THE GIVEN POLYGON. GIVEN POLYGON.
Ex. 4) FIND Ex. 4) FIND ? ?. .
Polygon Exterior Angle Polygon Exterior Angle- -Sum Theorem Sum Theorem The sum of the measures of the exterior angles of a The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. polygon, one at each vertex, is 360.
Vocabulary Vocabulary Equilateral Polygon Equilateral Polygon all sides congruent. all sides congruent. Equiangular Polygon Equiangular Polygon all angles congruent all angles congruent Regular Polygon Regular Polygon both equilateral and equiangular. both equilateral and equiangular.
Ex. 5 Ex. 5) Find the measure of an interior angle Find the measure of an interior angle and an exterior angle of each REGULAR and an exterior angle of each REGULAR polygon. polygon.
