1. ANGLES OF POLYGONS SPI 3108.4.3 SPI 3108.4.3 Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons. JIM SMITH JCHS

2. POLYGONS NOT POLYGONS

3. CONCAVE CONVEX TRY THE PEGBOARD AND RUBBER BAND TEST

4. NAMES OF POLYGONS SIDES SIDES TRIANGLE 3 QUADRILATERAL 4 PENTAGON 5 HEXAGON 6 HEPTAGON 7 OCTAGON 8 NONAGON 9 DECAGON 10 DODECAGON 12 N – GON N SEE PAGE 46 IN TEXTBOOK

5. INTERIOR ANGLE SUM OF CONVEX POLYGONS FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 6 SIDES = 4 TRIANGLES

6. INTERIOR ANGLE SUM FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 4 SIDES = 2 TRIANGLES

7. INTERIOR ANGLE SUM FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 8 SIDES = 6 TRIANGLES

8. INTERIOR ANGLE SUM EACH TRIANGLE HAS 180 DEGREES IF N IS THE NUMBER OF SIDES THEN: (N – 2 ) 180 = INT ANGLE SUM (N – 2 ) 180 = INT ANGLE SUM

9. 1 2 3 4 5 INT ANGLE SUM = ( 5 – 2 ) 180 ( 3 ) 180 = 540 DEGREES

10. REGULAR POLYGONS REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL ANGLES SO WE CAN FIND THE MEASURE OF EACH INTERIOR ANGLE REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL ANGLES SO WE CAN FIND THE MEASURE OF EACH INTERIOR ANGLE

11. EACH INTERIOR ANGLE OF A REGULAR POLYGON = (N – 2 ) 180 N REMEMBER N = NUMBER OF SIDES

12. REGULAR HEXAGON INT ANGLE SUM = (6 – 2 ) 180 = 720 EACH INT ANGLE = 720 = 120 6

13. ALL POLYGONS ALL POLYGONS HAVE AN EXTERIOR HAVE AN EXTERIOR ANGLE SUM OF ANGLE SUM OF 360 360 EXTERIOR ANGLE EXTERIOR ANGLE SUM THE MEASURE OF EACH EXTERIOR ANGLE OF A REGULAR POLYGON IS 360 N