1. Exploring Polygons

2. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. The following are examples of polygons:

3. The figures below are not polygons. Can you tell why?

4. Regular Polygons A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The following are examples of regular polygons: Would a square be a regular polygon? A rectangle?

5. The following are not examples of regular polygons: How do you know?

6. Triangles All three-sided polygons. There are many special types of triangles.

7. Quadrilateral A four-sided polygon.

8. Angles in quadrilaterals… Quadrilaterals have four sides and four angles. The sum of the measures of the angles is 360°. Find the value of x in the quadrilateral below x° + 105° + 80° + 95° = 360° Add 105°, 80°, and 95°. x° + 280° = 360° THINK: What measure added to 280° equals 360°? 80° + 280° = 360° x° = 80°

9. Find the value of x in each quadrilateral.

10. A rectangle has opposite sides congruent and parallel, and all right angles. Are rectangles a kind of quadrilateral? How do you know?

11. A square has all sides congruent, opposite sides parallel, and all right angles. Are squares a kind of rectangle? How do you know?

12. A parallelogram has opposite sides congruent and parallel, and opposite angles congruent. Are parallelograms a kind of rectangle? How do you know?

13. A rhombus has all sides congruent, opposite sides parallel, and opposite angles congruent. How are rhombuses and squares similar? How are rhombuses and squares different?

14. A trapezoid has exactly one pair of opposite sides parallel. There are special types of trapezoids ….that’s for another day!

15. Classify each quadrilateral.

16. Pentagon A five-sided polygon a regular pentagon an irregular pentagon

17. Hexagon A six-sided polygon. a regular hexagon an irregular hexagon

18. Heptagon A seven-sided polygon A regular heptagon an irregular heptagon

19. Octagon An eight-sided polygon. A regular octagon An irregular octagon

20. Nonagon A nine-sided polygon. A regular nonagon An irregular nonagon

21. Decagon A ten-sided polygon. A regular decagon An irregular decagon