Post on 03-Jan-2016
Triangle Fundamentals 1
Triangle Fundamentals
Triangle Fundamentals 2
Naming Triangles
For example, we can call the following triangle:
Triangles are named by using its vertices.
∆ABC ∆BAC
∆CAB ∆CBA∆BCA
∆ACB
A
B
C
Triangle 4
Classifying Triangles by Sides
Equilateral:
Scalene: A triangle in which all 3 sides are different lengths.
Isosceles: A triangle in which at least 2 sides are equal.
A triangle in which all 3 sides are equal.
AB
= 3
.02
cm
AC
= 3.15 cm
BC = 3.55 cm
A
B CAB =
3.47
cmAC = 3.47 cm
BC = 5.16 cmBC
A
HI = 3.70 cm
G
H I
GH = 3.70 cm
GI = 3.70 cm
Triangle Fundamentals 5
Classifying Triangles by Angles
Acute:
Obtuse:
A triangle in which all 3 angles are less than 90˚.
A triangle in which one and only one angle is greater than 90˚& less than 180˚
108
44
28 B
C
A
57 47
76
G
H I
Lesson 3-1: Triangle Fundamentals
6
Classifying Triangles by Angles
Right:
Equiangular:
A triangle in which one and only one angle is 90˚
A triangle in which all 3 angles are the same measure.
34
56
90B C
A
60
6060C
B
A
Triangle Fundamentals 7
polygons
Classification by Sides with Flow Charts & Venn Diagrams
triangles
Scalene
Equilateral
Isosceles
Triangle
Polygon
scalene
isosceles
equilateral
Triangle Fundamentals 8
polygons
Classification by Angles with Flow Charts & Venn Diagrams
triangles
Right
Equiangular
Acute
Triangle
Polygon
right
acute
equiangular
Obtuse
obtuse
Triangle Fundamentals 9
Theorems
The sum of the interior angles in a triangle is 180˚.
Triangle Sum Theorem:
B
A C
32
1
Triangle Fundamentals 10
Exterior Angle Theorem
The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Exterior AngleRemote Interior Angles A
BC
D
m ACD m A m B
Triangle Fundamentals 11
Exterior Angle Theorem
Given: Triangle ABC with Exterior angle ACDProve:
A
BC
D
m ACD m A m B
Triangle Fundamentals 12
Exterior Angle Theorem
Example:
(3x-22)x80
B
A DC
Find the mA.
3x - 22 = x + 80
3x – x = 80 + 22
2x = 102
mA = x = 51°
Homework
HW pg 221 # 1 to 6, 17, 18, 19 pg 222 #32 to 37
Triangle Fundamentals 13