2. A polygon is a closed figure formed by three or more line segments that do not cross. A triangle is a polygon with three sides. The sum of the measures of a triangle is 180°. There are two ways to classify triangles: By the number of congruent sides they have or by their angle measures. Example: 30° 80° 70°

3. Classifying Triangles by Sides Some types of triangles are shown below. TypeExampleProperties Scalene triangle A scalene triangle is a triangle with no congruent sides. No angles are congruent No sides are congruent Isosceles triangle An isosceles triangle is a triangle with at least two congruent sides. *at least two congruent sides *the angles opposite congruent sides have equal measure. Therefore, two angles, called base angles, are congruent Equilateral Triangle An equilateral triangle is a triangle with three congruent sides. All sides are congruent The angles opposite congruent sides have equal measures, Therefore, all angles are congruent.

4. The triangle has two sides that are congruent, so the triangle is an____________________. Example: Classify the triangle by its sides. Isosceles triangle

5. An equilateral triangle has one side with length 10 inches. What are the lengths of the other two sides? An equilateral triangle is a triangle with three congruent side, therefore, the length of the other two sides are also_______________. Example 1 10 inches

6. Classify the triangle by its sides. Quick Check 1 scalene 1a An equilateral triangle has one side with length 8 m. What are the lengths of the other two sides? 8 m 1b

7. Classifying Triangles by Angles Some types of triangles are shown below. TypeExampleProperties Right Triangle A right triangle is a triangle with one right angle * Exactly on angle is a right angle. The other two angles are acute. The acute angles are complementary Acute triangle A triangle with three acute angles *all angles are acute angles Obtuse triangle A triangle with one obtuse angle * Exactly one angle is an obtuse angles. The other two angles are acute Equiangular triangle A triangle with three congruent angles *all angles are acute *all angles are congruent *the sides opposite congruent angles have equal lengths. Therefore, all sides are congruent.

8. The triangle has a right angle, so the triangle is a ___________________________. Example: Classify the triangle by its angle measures. right triangle 38°52°

9. A triangle has two angles that measure 60°. What is the measure of the third angle? What is the classification of triangle by its angle measures? The sum of all the measures of the angles of a triangle is 180°. We can use an equation to find the measure of the third angle. Let x = the measure of the third angle. X + 60° + 60° = 180° X + 120° = 180° X = Since the triangle has three angles that are congruent, the triangle is an ____________________. Example 2 60° equiangular triangle

10. Classify the triangle by its angle measures. Quick Check 2 Acute triangle 2a A triangle has two angles that measure 48° and 37°. What is the measure of the third angle? What is the classification of the triangle by its angle measures? 48 + 37 = 85 2b 62° 72°46° 48 37 95 180 – 85 = 95Obtuse triangle

11. A quadrilateral is a polygon with four sides. The sum of the measures of the angles of a quadrilateral is_____________________. Quadrilaterals can be classified based on the information about their sides and angles. Some types of quadrilaterals are shown below. Example: 80° 100° 110° 360° 70° Using Properties to Classify Quadrilaterals.

12. TypeExampleProperties Parallelogram A parallelogram is a quadrilateral with two pairs of parallel sides. *opposite sides are parallel *opposite sides are congruent Rectangle A rectangle is a parallelogram with four right angles. * a rectangle has all the properties of a parallelogram *all angles are right angles *adjacent sides form right angles Rhombus A rhombus is a parallelogram with four congruent sides *a rhombus has all the properties of a parallelogram *all sides are congruent

13. TypeExampleProperties Square A square is a parallelogram with four right angles and four congruent angles A square has all the properties of a parallelogram *a square has all the properties of a rectangle *a square has all the properties of a rhombus Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. *exactly one pair of opposite sides is parallel

14. pentagon5 sides hexagon6 sides octagon8 sides decagon10 sides regular polygonSides and angles are congruent example regular pentagon irregular pentagon

15. List all the triangles pictured below that fit each description. EF D 1.Isosceles triangle_______________ 2.Equilateral triangle______________ 3.Scalene triangle________________ 4.Acute triangle__________________ 5.Obtuse triangle_________________ 6.Right isosceles triangle___________ CB A JL K O M N GI H

16. Circle all the names that are true for each figure. 7. Hexagon Quadrilateral Octagon polygon

17. Circle all the names that are true for each figure. 8. rhombus parallelogram quadrilateral Regular polygon

18. Circle all the names that are true for each figure. 9. pentagon hexagon Octagon polygon

19. Circle all the names that are true for each figure. 10. quadrilateral parallelogram square rectangle

20. Draw a figure to fit each description. 11. An obtuse scalene triangle

21. Draw a figure to fit each description. 12. An isosceles trapezoid

22. Draw a figure to fit each description. 13. A quadrilateral that is not a square but has all sides equal

23. Draw a figure to fit each description. 14. A regular hexagon

24. 15. Can an equilateral triangle be a right triangle? Explain.

25. TrianglesQuadrilaterals123456

26. 1. A triangle has two angles that measure 45° and 55°. What is the measure of the third angle? HOMEWORK A80° B180° C90° D55°

27. 2. Which of the following names could NOT describe a triangle with two congruent sides? HOMEWORK FIsosceles triangle GScalene triangle HRight triangle JAcute triangle

28. 3. Which of the following triangles best describes the triangle with the given measures? HOMEWORK ARight scalene triangle BAcute equilateral triangle CObtuse equilateral triangle DRight Isosceles triangle 3 5 4

29. 4. Which statement is always true about an isosceles triangle? HOMEWORK FIt has 3 congruent angles GIt has at least 2 congruent sides HIt has 3 congruent sides JIt has no congruent sides

30. 5. Mr. Richardson bought a new triangular sail for his sailboat. Which of the following triangles best describes the triangular sail with the given measures? HOMEWORK Aobtuse isosceles triangles Bright scalene triangle Cacute equilateral triangle DAcute isosceles triangle 50°

31. 6. Which statement is NOT true about an equiangular triangle? HOMEWORK FThe sum of the measures of the 3 angles is 180° GIt has exactly 2 congruent angles HIt has 3 congruent angles JIt has 3 congruent sides

32. 1. A diamond is cut to the following shape. Which of the following best describes the quadrilateral with the given measurements? HOMEWORK Asquare Brhombus Ckite Dparallelogram

33. 2. The profile of a tent is shown below. Which of the following best describes the triangle with the given measurements? HOMEWORK Fright isosceles Gacute isosceles Hobtuse isosceles Jacute equilateral 10 ft 7 ft 43°

34. 3. A rearview mirror on a new car is shaped as shown below. Which of the following best describes the quadrilateral with the given measurements? HOMEWORK Arectangle Bsquare Crhombus Dtrapezoid 130° 500°

35. 4. A jet plane’s wing is shown below. Which of the following best describes the triangle as shown? HOMEWORK Fright isosceles Gright scalene Hacute isosceles Jacute scalene 56°

36. m  ABC = m  C = B C A 110° 50°

37. 1. Which statement is always true about an isosceles triangle? HOMEWORK AIt has 3 congruent angles BIt has 1 right angle CIt has 2 congruent angles DIt has exactly 1 acute angle

38. 2. Which statement is always true about a pentagon? HOMEWORK AIt has 5 congruent angles BIt has 5 obtuse angles CThe sum of all the angles is 540 DIt has exactly 6 sides

39. 3. Which statement is always true about a quadrilateral? HOMEWORK AIt has exactly 4 congruent angles BIt has 1 right angle CThe sum of all the angles is 360 DIt has exactly 1 acute angle

40. 4. Which statement is always true about a right triangle? HOMEWORK AIt has exactly 3 congruent angles BIt has 1 right angle CIt has exactly 2 congruent sides DIt has 2 obtuse angles

41. NO WARM UP Get out your homework! Friday, January 12

42. 1. Which of the following statements is always true about quadrilaterals? HOMEWORK AAll sides are congruent BAll angles are congruent CThe sum of the measures of the angles is 360° Dopposite sides are parallel

43. 2. Which of the following statements is always true? HOMEWORK FA trapezoid is a parallelogram GA square is a rectangle HA rectangle is a square JA quadrilateral is a parallelogram

44. 3. Which of the following statements is NOT a name for the figure? HOMEWORK Aparallelogram Bquadrilateral Crectangle Drhombus 4 10

45. 4. How many parallel lines does a trapeziod have? HOMEWORK F1F1 G3G3 H3H3 J4J4

46. 5. How many congruent sides does a rhombus have? HOMEWORK A1A1 B3B3 C3C3 D4D4

47. 6. Which of the following names is the best name for the quadrilateral? HOMEWORK Frectangle Grhombus Hparallelogram Jsquare 5 5

48. 1. A triangle is a ________________ with three sides. HOMEWORK

49. 2. A polygon with four sides is a _________________ HOMEWORK

50. 3.A polygon with five sides is a HOMEWORK

51. 4.A hexagon is a polygon with six sides and six HOMEWORK

52. 5.A polygon with eight sides is an HOMEWORK

53. 6.A polygon with ten sides is a HOMEWORK

54. 7.A triangle with no congruent sides is a ________________ triangle. HOMEWORK

55. 8. A triangle (or trapezoid) with two congruent sides is HOMEWORK

56. 9.A polygon with all sides congruent is HOMEWORK

57. 10.A triangle with a 90° angle is a ______________ triangle HOMEWORK

58. 11.A quadrilateral whose opposite sides are parallel is a HOMEWORK

59. 12.A parallelogram with four right angles is a HOMEWORK

60. 13.A quadrilateral with one pair of parallel sides is a HOMEWORK

61. 14.A parallelogram which is equilateral is a HOMEWORK

62. 15.A rectangle which is equilateral is a HOMEWORK