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
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
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
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
