1. Triangle Fundamentals

2. Triangle Fundamentals
Naming Triangles
Triangles are named by using its vertices.
For example, we can call the following triangle: A B C
∆ABC
∆ACB
∆BAC
∆BCA
∆CAB
∆CBA
Triangle Fundamentals

3. Lesson 3-1: Triangle Fundamentals
Opposite Sides and Angles
Opposite Sides:
Side opposite to A :
Side opposite to B :
Side opposite to C :
Opposite Angles:
Angle opposite to : A
Angle opposite to : B
Angle opposite to : C
Lesson 3-1: Triangle Fundamentals

4. Classifying Triangles by Sides
Scalene:
A triangle in which all 3 sides are different lengths. BC =
5.16 cm B C A BC =
3.55 cm A B C
AB = 3.47 cm
AC = 3.47 cm
AB = 3.02 cm
AC = 3.15 cm
Isosceles:
A triangle in which at least 2 sides are equal. HI =
3.70 cm G H I
Equilateral:
A triangle in which all 3 sides are equal.
GI = 3.70 cm
GH = 3.70 cm
Triangle

5. Classifying Triangles by Angles
Acute:
A triangle in which all 3 angles are less than 90˚. 57 47 76 G H I
Obtuse:
108 44 28 B C A
A triangle in which one and only one angle is greater than 90˚& less than 180˚
Triangle Fundamentals

6. Classifying Triangles by Angles
Right:
A triangle in which one and only one angle is 90˚
Equiangular:
A triangle in which all 3 angles are the same measure.
Lesson 3-1: Triangle Fundamentals

7. Triangle Fundamentals
Classification by Sides
with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
scalene
isosceles
Scalene
Isosceles
equilateral
Equilateral
Triangle Fundamentals

8. Triangle Fundamentals
Classification by Angles
with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
right
acute
equiangular
Right
Obtuse
Acute
obtuse
Equiangular
Triangle Fundamentals

9. Triangle Fundamentals
Theorems
Triangle Sum Theorem:
The sum of the interior angles in a triangle is 180˚. B 1 3 2 C A
Triangle Fundamentals

10. Triangle Fundamentals
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.
Remote Interior Angles A
Exterior Angle D B C
Triangle Fundamentals

11. Triangle Fundamentals
Exterior Angle Theorem
Given: Triangle ABC with Exterior angle ACD
Prove: A D B C
Triangle Fundamentals

12. Triangle Fundamentals
Exterior Angle Theorem
Example:
Find the mA.
3x - 22 = x + 80
3x – x =
2x = 102
mA = x = 51°
Triangle Fundamentals

13. Triangle Fundamentals
Homework
HW pg 221 # 1 to 6, 17, 18, 19
pg 222 #32 to 37
Triangle Fundamentals