1. Section 3-4
Angles of a Triangle

2. Triangle:
The figure formed by three segments joining three noncollinear points
The segments are called the sides of a triangle
Each of the three points is a vertex of the triangle

3. For Example:
sides:
vertices:
angles: or or or
C, D, E

4. Triangles are classified by their sides and angles.
1) By their angles:
a. acute : three acute angles
b. obtuse : one obtuse 
c. right : one right 
d. equiangular : all ’s are 

5. Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle

6. c. equilateral : all sides are 
2) By their sides.
a. scalene : no sides are  ;
all different lengths.
b. isosceles : at least sides are .
c. equilateral : all sides are 

7. Isosceles Triangle
Equilateral Triangle
Scalene Triangle

8. The sum of the measures of the angles of a triangle is 180.
Theorem 3-11:
The sum of the measures of the angles of a triangle is 180. 1 3 2

9. Remote interior angles
Theorem 3-12
The measure of an exterior angle of a triangle equals the sum of the measure of the two remote interior angles
Remote interior angles
Exterior Angle

10. 3 4 1 2

11. a statement that can be proved easily by applying a theorem
Corollary:
a statement that can be proved easily by applying a theorem

12. Corollaries:
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
Each angle of an equiangular triangle has measure 60.
In a triangle, there can be at most one right angle or obtuse angle.
The acute angles of a right triangle are complementary.