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Exploring Polygon Relationships and Theorems in Geometry

Identify, describe, and apply relationships and theorems of triangles, quadrilaterals, and other polygons. Learn about concave, convex polygons and use the pegboard and rubber band test. Understand interior and exterior angle sums and explore regular polygons.

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Exploring Polygon Relationships and Theorems in Geometry

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  1. ANGLESOFPOLYGONS 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 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

  9. 2 3 1 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

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

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