Download Section 4

Section 4.1 - It’s Really All About the Triangle
Classifying Triangles – this has everything to do with their sides and angle:
Classifying by Sides!
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
No congruent sides
At least 2 congruent sides
3 congruent sides
Can a triangle have more than 3 congruent sides?
Is an Isosceles Triangle also an Equilateral Triangle?
Is an Equilateral Triangle also an Isosceles Triangle?
Classifying by Angles!
Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle
3 acute angles
1 right angle
1 obtuse angle
3 congruent angles
Theorem 4.1 – Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 1800.
Find x & y
3y
x
34
72
Can a triangle be acute and right?
63
(2y+10)
Can a triangle be right and obtuse?
An equiangular triangle is also what type of triangle?
External Angle Theater
Q-Man: What are these External Angles of which you speak?
A-Man: They are the angles which form a linear pair with the internal angles.
Q-Man: How do you make one?
A-Man: You extend one of sides of the triangles outward like so:
Q-Man: Is there anything interesting about them?
A-Man: Yes! There is…..
Theorem 4.2
Exterior Angle Theorem
The measure of an external angle of a triangle is equal to the sum of the
measures of the two nonadjacent interior angles.
Q-Man: I don’t believe you. You are a dirty liar!
A-Man: Don’t call me a liar you idiot. I can prove it….
Given: 1, 2, and 3 are internal angles of a triangle
3 and 4 are a linear pair
1
Prove: m1  m2  m4
Statement
2
Reason
Q-Man: I guess you proved me wrong.
A-Man: That I did. That I did.
Find x & y:
87
76
97
x
67
y
3
4