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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