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ANGLES OF POLYGONS. SECTION 8-1. JIM SMITH JCHS. POLYGONS. NOT POLYGONS. CONCAVE. CONVEX. TRY THE PEGBOARD AND RUBBER BAND TEST. NAMES OF POLYGONS. SIDES TRIANGLE 3 QUADRILATERAL 4 PENTAGON 5 HEXAGON 6 - PowerPoint PPT Presentation
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ANGLESANGLES OFOF POLYGONSPOLYGONS
SECTION 8-1SECTION 8-1
JIM SMITH JCHS
POLYGONS
NOT POLYGONS
CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST
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
INTERIOR ANGLE SUMOF CONVEX POLYGONS
FIND THE NUMBEROF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
6 SIDES = 4 TRIANGLES
INTERIOR ANGLE SUM
FIND THE NUMBEROF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
4 SIDES = 2 TRIANGLES
INTERIOR ANGLE SUM
FIND THE NUMBEROF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
8 SIDES = 6 TRIANGLES
INTERIOR ANGLE SUM
EACH TRIANGLE HAS 180°EACH TRIANGLE HAS 180°
IF N IS THE NUMBER OF SIDES IF N IS THE NUMBER OF SIDES THEN:THEN:
INT ANGLE SUM =INT ANGLE SUM =
(N – 2 ) 180°(N – 2 ) 180°
1
23
4
5
INT ANGLE SUM = ( 5 – 2 ) 180°
( 3 ) 180° = 540°
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
EACH INTERIOR ANGLE OFA REGULAR POLYGON =
(N – 2 ) 180(N – 2 ) 180 NNREMEMBER N = NUMBER OF SIDES
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
ALL POLYGONSALL POLYGONS HAVE AN HAVE AN EXTERIOREXTERIOR ANGLE SUMANGLE SUM OF OF
360°360°
EXTERIOR ANGLEEXTERIOR ANGLE
EXTERIOR ANGLE SUM
THE MEASURE OF EACH EXTERIORANGLE OF A REGULAR POLYGON IS
360° N
NAME ____________NAME ____________# SIDES ____# SIDES ____88________________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE _________EACH EXT ANGLE _________
NAME NAME OctagonOctagon
# SIDES ____# SIDES ____88________________
INT ANGLE SUM INT ANGLE SUM 6 x 180 =6 x 180 = 1080°1080°
EACH INT ANGLE EACH INT ANGLE 1080 / 8 =1080 / 8 = 135°135°
EXT ANGLE SUM EXT ANGLE SUM 360°360°
EACH EXT ANGLE EACH EXT ANGLE 360 / 8 =360 / 8 = 45°45°
NAME NAME DECAGONDECAGON# SIDES ____________# SIDES ____________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE _________EACH EXT ANGLE _________
NAME NAME DECAGONDECAGON
# SIDES # SIDES 1010 INT ANGLE SUM INT ANGLE SUM 8 x 180 = 8 x 180 = 1440°1440° EACH INT ANGLE EACH INT ANGLE 1440 / 10 = 1440 / 10 = 144°144° EXT ANGLE SUM EXT ANGLE SUM 360°360°
EACH EXT ANGLE EACH EXT ANGLE 360 / 10 = 360 / 10 = 36°36°
NAME ____________NAME ____________# SIDES ____________# SIDES ____________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE EACH EXT ANGLE 60______60______
NAME NAME HEXAGONHEXAGON
# SIDES # SIDES 360 / 60 = 360 / 60 = 66
INT ANGLE SUM INT ANGLE SUM (6-2) X 180 =(6-2) X 180 = 720°720°
EACH INT ANGLE EACH INT ANGLE 720 / 6 =720 / 6 = 120° 120°
EXT ANGLE SUM EXT ANGLE SUM 360°360°
EACH EXT ANGLE EACH EXT ANGLE 60 60
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