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# Integrated Math 2 Section 5-4

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Properties of Triangles

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• ### Integrated Math 2 Section 5-4

1. 1. Section 5-4 Properties of Triangles
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, navigation
3. 3. Vocabulary 1. Triangle: 2. Vertex: 3. Congruent Sides: 4. Congruent Angles: 5. Exterior Angle: 6. Base Angles:
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:
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:
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:
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:
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:
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:
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 sides
11. 11. A B C
12. 12. A B C Vertices:
13. 13. A B C Vertices: A, B, C
14. 14. A B C Vertices: A, B, C Sides:
15. 15. A B C Vertices: A, B, C Sides: AB, BC , AC
16. 16. A B C Vertices: A, B, C Sides: AB, BC , AC Angles:
17. 17. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠C
18. 18. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠C or
19. 19. A B C Vertices: A, B, C Sides: AB, BC , AC Angles: ∠A,∠B,∠C or ∠BAC ,∠ABC ,∠ACB
20. 20. Triangle Vocabulary Scalene Triangle: Acute Triangle: Isosceles Triangle: Equilateral Triangle: Obtuse Triangle: Right Triangle:
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:
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:
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:
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:
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:
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 legs
27. 27. Properties of Triangles
28. 28. Properties of Triangles 1. The sum of the angles in a triangle is 180 degrees
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 side
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 angle
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 angles
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 congruent
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° G
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° G
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° G
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° G
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° G
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° G
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° G
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° G
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° G
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 G
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 G
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 G
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 G
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 D
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 D
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 D
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 D
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 D
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∠RDF
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 −57
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°
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°
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°
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°
57. 57. Homework
58. 58. Homework p. 208 #1-33 odd “Change your thoughts and you change your world.” - Norman Vincent Peale