1. curve—continuous set of points (includes lines)

2. simple curves—do not intersect themselves

3. closed curves—start and end at same point

4. simple closed simple, not closed simple closed closed, not simple

5. A polygon is a simple closed plane figure made up of line segments. Polygon

6. A convex polygon is a polygon in which all interior angles have measures less than 180°. Convex Polygon

7. A concave polygon is a polygon in which at least one interior angle has a measure greater than 180°. Concave Polygon

8. Types of Polygons convex concave

9. side—segment making up part of a polygon

10. vertex—corner of a polygon; where two sides meet

11. Number of Sides Name quadrilateral triangle pentagon hexagon heptagon 3 3 4 4 5 5 6 6 7 7

12. Number of Sides Name nonagon octagon decagon dodecagon n-gon 8 8 9 9 10 12 n n

13. regular polygon—all sides same length, all angles same measure

14. Example 1 Name each polygon and indicate whether it is regular. ABCD is a quadrilateral. DD AABB CC

15. Name each polygon and indicate whether it is regular. EFGHIJ is a regular hexagon. JJ EE GG HH II FF Example 1

16. scalene triangle: A triangle with no two sides equal in length.

17. isosceles triangle: A triangle with at least two sides equal in length.

18. equilateral triangle: A triangle with all sides equal in length.

19. acute triangle: three acute angles 60° 75° 45°

20. right triangle: one right angle 50° 40°

21. obtuse triangle: one obtuse angle 20° 30° 130°

22. Classify each triangle according to the measures of its angles and the lengths of its sides. Example 2

23. BB AA CC ABC is obtuse scalene.

24. EE DDFF DEF is right isosceles.

25. HH GGII GHI is acute equilateral.

26. Theorem In any triangle, the sum of the measures of the angles is 180°: in ABC m A + m B + m C = 180°.

27. Write and solve an equation to find m X. XX YYZZ ?? 116° 22° Example 3

28. m X + m Y + m Z = 180 m X + 116 + 22 = 180 m X + 138 = 180 m X = 42° Example 3

29. A quadrilateral is a four-sided polygon. Quadrilateral

30. A trapezoid is a quadrilateral with at least one pair of parallel sides. Trapezoid

31. A parallelogram is a quadrilateral with two pairs of parallel sides. Parallelogram

32. A rectangle is a parallelogram with four right angles. Rectangle

33. A rhombus is a parallelogram with four congruent sides. Rhombus

34. A square is a rectangle with four congruent sides. Square

35. A diagonal is a line segment joining any two nonadjacent vertices of a polygon. Diagonal

36. number of diagonals from one vertex number of sides, n number of triangles formed Triangle sum of angle measures 3 3 1 1 180°

37. number of diagonals from one vertex number of sides, n number of triangles formed Quadrilateral sum of angle measures 4 4 2 2 2(180) = 360°

38. number of diagonals from one vertex number of sides, n number of triangles formed Pentagon sum of angle measures 5 5 3 3 3(180) = 540°

39. number of diagonals from one vertex number of sides, n number of triangles formed Hexagon sum of angle measures 6 6 4 4 4(180) = 720°

40. Find the sum of the measures of the angles in a regular octagon. 6(180) = 1,080° Example 4

41. Find the measure of each angle in a regular octagon. = 135° 1,080 8 Example 4

42. Write and solve an equation to find m A. BB AA CC 120° 55° DD 80° Example 5

43. m A + 80 + 55 + 120 = 360 m A + 255 = 360 m A = 105° m A + 255 – 255 = 360 – 255 Example 5