Section 5-4              Properties of TrianglesTue, Jan 25
Essential Questions              How do you classify triangles according to their sides and              angles?          ...
Vocabulary      1. Triangle:      2. Vertex:      3. Congruent Sides:      4. Congruent Angles:      5. Exterior Angle:   ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex:      3. Congruent Sides:      4. Co...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
Vocabulary      1. Triangle: A shape with three sides and three angles      2. Vertex: The point where two sides meet     ...
A              B                      CTue, Jan 25
A              B                              C                  Vertices:Tue, Jan 25
A              B                                      C                  Vertices: A, B, CTue, Jan 25
A              B                                      C                  Vertices: A, B, C                  Sides:Tue, Jan...
A              B                                       C                  Vertices: A, B, C                  Sides: AB, BC...
A              B                                       C                  Vertices: A, B, C                  Sides: AB, BC...
A              B                                       C                  Vertices: A, B, C                  Sides: AB, BC...
A              B                                       C                  Vertices: A, B, C                  Sides: AB, BC...
A              B                                        C                   Vertices: A, B, C                   Sides: AB,...
Triangle Vocabulary      Scalene Triangle:      Acute Triangle:      Isosceles Triangle:      Equilateral Triangle:      O...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Triangle Vocabulary      Scalene Triangle: A triangle where all three sides have different lengths           and all three...
Properties of TrianglesTue, Jan 25
Properties of Triangles        1. The sum of the angles in a triangle is 180 degreesTue, Jan 25
Properties of Triangles        1. The sum of the angles in a triangle is 180 degrees        2. If you add two sides of a t...
Properties of Triangles        1. The sum of the angles in a triangle is 180 degrees        2. If you add two sides of a t...
Properties of Triangles        1. The sum of the angles in a triangle is 180 degrees        2. If you add two sides of a t...
Properties of Triangles        1. The sum of the angles in a triangle is 180 degrees        2. If you add two sides of a t...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 1              For the two triangles, list the sides from shortest to longest.                                    ...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Example 2         In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°.                        Find the measures of th...
Problem SetTue, Jan 25
Problem Set                              p. 208 #1-33 odd              “Change your thoughts and you change your world.”  ...
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Int Math 2 Section 5-4 1011

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Properties of Triangles

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Int Math 2 Section 5-4 1011

  1. 1. Section 5-4 Properties of TrianglesTue, Jan 25
  2. 2. Essential Questions How do you classify triangles according to their sides and angles? How do you identify and use properties of triangles? Where you’ll see this: Travel, interior design, navigationTue, Jan 25
  3. 3. Vocabulary 1. Triangle: 2. Vertex: 3. Congruent Sides: 4. Congruent Angles: 5. Exterior Angle: 6. Base Angles:Tue, Jan 25
  4. 4. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: 3. Congruent Sides: 4. Congruent Angles: 5. Exterior Angle: 6. Base Angles:Tue, Jan 25
  5. 5. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: 4. Congruent Angles: 5. Exterior Angle: 6. Base Angles:Tue, Jan 25
  6. 6. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: Sides that are the same length 4. Congruent Angles: 5. Exterior Angle: 6. Base Angles:Tue, Jan 25
  7. 7. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: Sides that are the same length 4. Congruent Angles: Angles with the same measure 5. Exterior Angle: 6. Base Angles:Tue, Jan 25
  8. 8. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: Sides that are the same length 4. Congruent Angles: Angles with the same measure 5. Exterior Angle: The angle formed by extending a side outside of the triangle 6. Base Angles:Tue, Jan 25
  9. 9. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: Sides that are the same length 4. Congruent Angles: Angles with the same measure 5. Exterior Angle: The angle formed by extending a side outside of the triangle R F P D 6. Base Angles:Tue, Jan 25
  10. 10. Vocabulary 1. Triangle: A shape with three sides and three angles 2. Vertex: The point where two sides meet 3. Congruent Sides: Sides that are the same length 4. Congruent Angles: Angles with the same measure 5. Exterior Angle: The angle formed by extending a side outside of the triangle R F P D 6. Base Angles: In an isosceles triangle, the angles that are opposite of the congruent sidesTue, Jan 25
  11. 11. A B CTue, Jan 25
  12. 12. A B C Vertices:Tue, Jan 25
  13. 13. A B C Vertices: A, B, CTue, Jan 25
  14. 14. A B C Vertices: A, B, C Sides:Tue, Jan 25
  15. 15. A B C Vertices: A, B, C Sides: AB, BC , ACTue, Jan 25
  16. 16. A B C Vertices: A, B, C Sides: AB, BC , AC Angles:Tue, Jan 25
  17. 17. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠CTue, Jan 25
  18. 18. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠C orTue, Jan 25
  19. 19. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠C or ∠BAC ,∠ABC ,∠ACBTue, Jan 25
  20. 20. Triangle Vocabulary Scalene Triangle: Acute Triangle: Isosceles Triangle: Equilateral Triangle: Obtuse Triangle: Right Triangle:Tue, Jan 25
  21. 21. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: Isosceles Triangle: Equilateral Triangle: Obtuse Triangle: Right Triangle:Tue, Jan 25
  22. 22. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: All three angles are less than 90 degrees Isosceles Triangle: Equilateral Triangle: Obtuse Triangle: Right Triangle:Tue, Jan 25
  23. 23. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: All three angles are less than 90 degrees Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides Equilateral Triangle: Obtuse Triangle: Right Triangle:Tue, Jan 25
  24. 24. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: All three angles are less than 90 degrees Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides Equilateral Triangle: All sides are congruent, as are all angles Obtuse Triangle: Right Triangle:Tue, Jan 25
  25. 25. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: All three angles are less than 90 degrees Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides Equilateral Triangle: All sides are congruent, as are all angles Obtuse Triangle: Has one angle that is greater than 90 degrees Right Triangle:Tue, Jan 25
  26. 26. Triangle Vocabulary Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures Acute Triangle: All three angles are less than 90 degrees Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides Equilateral Triangle: All sides are congruent, as are all angles Obtuse Triangle: Has one angle that is greater than 90 degrees Right Triangle: Had a right angle; The side opposite of the right angle is the hypotenuse (longest side) and the other sides are the legsTue, Jan 25
  27. 27. Properties of TrianglesTue, Jan 25
  28. 28. Properties of Triangles 1. The sum of the angles in a triangle is 180 degreesTue, Jan 25
  29. 29. Properties of Triangles 1. The sum of the angles in a triangle is 180 degrees 2. If you add two sides of a triangle, the sum will be bigger than the length of the third sideTue, Jan 25
  30. 30. Properties of Triangles 1. The sum of the angles in a triangle is 180 degrees 2. If you add two sides of a triangle, the sum will be bigger than the length of the third side 3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angleTue, Jan 25
  31. 31. Properties of Triangles 1. The sum of the angles in a triangle is 180 degrees 2. If you add two sides of a triangle, the sum will be bigger than the length of the third side 3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle 4. The exterior angle formed at one vertex equals the sum of the other two interior anglesTue, Jan 25
  32. 32. Properties of Triangles 1. The sum of the angles in a triangle is 180 degrees 2. If you add two sides of a triangle, the sum will be bigger than the length of the third side 3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle 4. The exterior angle formed at one vertex equals the sum of the other two interior angles 5. If two sides are congruent, then the angles opposite those sides are congruentTue, Jan 25
  33. 33. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° F E m∠HGF = 75° m∠GFH = 55° m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  34. 34. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 F E m∠HGF = 75° m∠GFH = 55° m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  35. 35. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° m∠GFH = 55° m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  36. 36. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° m∠GFH = 55° #2 m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  37. 37. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  38. 38. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  39. 39. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° m∠EGF = 50° GTue, Jan 25
  40. 40. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° #1 m∠EGF = 50° GTue, Jan 25
  41. 41. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° #1 FG m∠EGF = 50° GTue, Jan 25
  42. 42. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° #1 FG m∠EGF = 50° #2 GTue, Jan 25
  43. 43. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° H m∠FEG = 40° #1 FG m∠EGF = 50° #2 FE GTue, Jan 25
  44. 44. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° #3 H m∠FEG = 40° #1 FG m∠EGF = 50° #2 FE GTue, Jan 25
  45. 45. Example 1 For the two triangles, list the sides from shortest to longest. m∠FHG = 50° #1 FG F E m∠HGF = 75° #3 FH m∠GFH = 55° #2 HG m∠GFE = 90° #3 GE H m∠FEG = 40° #1 FG m∠EGF = 50° #2 FE GTue, Jan 25
  46. 46. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R F P DTue, Jan 25
  47. 47. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R F P DTue, Jan 25
  48. 48. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD F P DTue, Jan 25
  49. 49. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 F P DTue, Jan 25
  50. 50. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P DTue, Jan 25
  51. 51. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RDP =180 − m∠RDFTue, Jan 25
  52. 52. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RDP =180 − m∠RDF =180 −57Tue, Jan 25
  53. 53. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RDP =180 − m∠RDF =180 −57 m∠RDP =123°Tue, Jan 25
  54. 54. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RPD =180 − m∠RDP − m∠DRP m∠RDP =180 − m∠RDF =180 −57 m∠RDP =123°Tue, Jan 25
  55. 55. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RPD =180 − m∠RDP − m∠DRP m∠RDP =180 − m∠RDF m∠RPD =180 −123− 24 =180 −57 m∠RDP =123°Tue, Jan 25
  56. 56. Example 2 In the figure, m∠RFD = 33°, m∠FRD = 90°, and m∠DRP = 24°. Find the measures of the other angles. R m∠RDF =180 − m∠DRF − m∠RFD m∠RDF =180 −33− 90 m∠RDF = 57° F P D m∠RPD =180 − m∠RDP − m∠DRP m∠RDP =180 − m∠RDF m∠RPD =180 −123− 24 =180 −57 m∠RPD = 33° m∠RDP =123°Tue, Jan 25
  57. 57. Problem SetTue, Jan 25
  58. 58. Problem Set p. 208 #1-33 odd “Change your thoughts and you change your world.” - Norman Vincent PealeTue, Jan 25

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