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

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 NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX

6 SIDES = 4 TRIANGLES

INTERIOR ANGLE SUM

FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX

4 SIDES = 2 TRIANGLES

INTERIOR ANGLE SUM

FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX

8 SIDES = 6 TRIANGLES

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

1

23

4

5

INT ANGLE SUM = ( 5 – 2 ) 180( 3 ) 180 = 540 DEGREES

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 NN

REMEMBER 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 360360

EXTERIOR ANGLEEXTERIOR ANGLE

EXTERIOR ANGLE SUM

THE MEASURE OF EACH EXTERIORANGLE OF A REGULAR POLYGONIS 360 N