angles of polygons spi 3108.4.3 spi 3108.4.3 identify, describe and/or apply the relationships and...
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ANGLESANGLES OFOF POLYGONSPOLYGONS
SPI 3108.4.3 SPI 3108.4.3 Identify, describe and/or apply the relationships Identify, describe and/or apply the relationships
and theorems involving different types of and theorems involving different types of triangles, quadrilaterals and other polygons.triangles, quadrilaterals and other polygons.
JIM SMITH JCHS
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POLYGONS
NOT POLYGONS
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CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST
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NAMES OF POLYGONSNAMES OF POLYGONS SIDES SIDES
TRIANGLE 3 TRIANGLE 3
QUADRILATERAL 4QUADRILATERAL 4
PENTAGON 5PENTAGON 5
HEXAGON 6HEXAGON 6
HEPTAGON 7HEPTAGON 7
OCTAGON 8OCTAGON 8
NONAGON 9NONAGON 9
DECAGON 10DECAGON 10
DODECAGON 12DODECAGON 12
N – GON NN – GON N
SEE PAGE 46 IN TEXTBOOK
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INTERIOR ANGLE SUMOF CONVEX POLYGONS
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
6 SIDES = 4 TRIANGLES
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INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
4 SIDES = 2 TRIANGLES
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INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
8 SIDES = 6 TRIANGLES
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INTERIOR ANGLE SUM
EACH TRIANGLE HAS 180 EACH TRIANGLE HAS 180 DEGREESDEGREES
IF N IS THE NUMBER OF SIDES IF N IS THE NUMBER OF SIDES THEN:THEN:
(N – 2 ) 180 = INT ANGLE (N – 2 ) 180 = INT ANGLE SUMSUM
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1
23
4
5
INT ANGLE SUM = ( 5 – 2 ) 180( 3 ) 180 = 540 DEGREES
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REGULAR POLYGONSREGULAR POLYGONS
REGULAR POLYGONSREGULAR POLYGONS HAVE EQUAL SIDES AND HAVE EQUAL SIDES AND EQUAL ANGLES SO WE EQUAL ANGLES SO WE CAN FIND THE MEASURE CAN FIND THE MEASURE OF OF EACHEACH INTERIOR ANGLE INTERIOR ANGLE
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EACH INTERIOR ANGLE OFA REGULAR POLYGON =
(N – 2 ) 180(N – 2 ) 180 NN
REMEMBER N = NUMBER OF SIDES
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REGULAR HEXAGONREGULAR HEXAGON
INT ANGLE SUM =INT ANGLE SUM =
(6 – 2 ) 180 =(6 – 2 ) 180 = 720720
EACH INT ANGLE = EACH INT ANGLE =
720720 = = 120120 66
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ALL POLYGONSALL POLYGONS HAVE AN HAVE AN EXTERIOREXTERIOR ANGLE SUMANGLE SUM OF OF 360360
EXTERIOR ANGLEEXTERIOR ANGLE
EXTERIOR ANGLE SUM
THE MEASURE OF EACH EXTERIORANGLE OF A REGULAR POLYGONIS 360 N