Properties of Triangles

1. Section 5-4
Properties of Triangles
Tue, Jan 25

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
Tue, Jan 25

3. Vocabulary
1. Triangle:
2. Vertex:
3. Congruent Sides:
4. Congruent Angles:
5. Exterior Angle:
6. Base Angles:
Tue, Jan 25

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. 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. 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. 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. 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. 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. 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
Tue, Jan 25

11. A
B
C
Tue, Jan 25

12. A
B
C
Vertices:
Tue, Jan 25

13. A
B
C
Vertices: A, B, C
Tue, Jan 25

14. A
B
C
Vertices: A, B, C
Sides:
Tue, Jan 25

15. A
B
C
Vertices: A, B, C
Sides: AB, BC , AC
Tue, Jan 25

16. A
B
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles:
Tue, Jan 25

17. A
B
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠C
Tue, Jan 25

18. A
B
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠C
or
Tue, Jan 25

19. A
B
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠C
or
∠BAC ,∠ABC ,∠ACB
Tue, Jan 25

20. Triangle Vocabulary
Scalene Triangle:
Acute Triangle:
Isosceles Triangle:
Equilateral Triangle:
Obtuse Triangle:
Right Triangle:
Tue, Jan 25

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. 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. 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. 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. 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. 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
Tue, Jan 25

27. Properties of Triangles
Tue, Jan 25

28. Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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
Tue, Jan 25

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. 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. 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. 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. Problem Set
Tue, Jan 25

58. Problem Set
p. 208 #1-33 odd
“Change your thoughts and you change your world.”
- Norman Vincent Peale
Tue, Jan 25