1. 6.1 Polygons

2. Objectives: Identify, name, and describe polygons. Identify, name, and describe polygons. Use the sum of the interior angles of a quadrilateral. Use the sum of the interior angles of a quadrilateral.

3. Polygon: Shape with: Shape with: 3 or more sides 3 or more sides Line segments only (no gaps, no crisscrossing) Line segments only (no gaps, no crisscrossing) Name using vertices: Name using vertices: Ex: PQRST or QPTSR Ex: PQRST or QPTSR SIDE

4. Ex# 1: Polygons Which are polygons? Which are polygons? Which are ot polygons? Which are ot polygons? A, B, C = polygons D, E, F = NOT polygons

5. Polygon names & Number of sides: MEMORIZE # of sidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon

6. Polygon names & Number of sides: MEMORIZE # of sidesName 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon

7. Convex or Concave?

11. Regular Polygon = Equilateral + Equiangular

12. YES Equilateral NOT Equiangular NOT Regular

13. Regular Polygon = Equilateral + Equiangular YES Equilateral NOT Equiangular NOT Regular

14. Regular Polygon = Equilateral + Equiangular YES Equilateral NOT Equiangular NOT Regular YES Equilateral NOT Equiangular NOT Regular

15. Regular Polygon = Equilateral + Equiangular YES Equilateral NOT Equiangular NOT Regular YES Equilateral NOT Equiangular NOT Regular

16. Regular Polygon = Equilateral + Equiangular YES Equilateral NOT Equiangular NOT Regular YES Equilateral NOT Equiangular NOT Regular YES Equilateral YES Equiangular YES Regular

17. Diagonals Join nonconsecutive vertices Join nonconsecutive vertices diagonals

18. Sum of Interior Angles Quadrilaterals are made of 2 triangles. Quadrilaterals are made of 2 triangles. (180° + 180°) = 360° (180° + 180°) = 360° 180° 360°

19. Theorem 6.1: Interior Angles of a Quadrilateral The sum of the interior angles is 360°. The sum of the interior angles is 360°. m  1 + m  2 + m  3 + m  4 = 360°

20. Ex. 4 Find x: Find x: x°+ 2x° + 70° + 80° = 360° 3x° + 150° = 360° 3x° + 150° = 360° 3x° = 210° 3x° = 210° x° = 70° x° = 70° 80° 70° x°x° 2x°

21. Ex. 4 m  Q and m  R : m  Q and m  R : m  Q = x° = 70° m  R = 2x°= 140° 80° 70° x°x° 2x°