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Section 3-4
Angles of a
Triangle
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
For Example:
C
sides:
CD, DE, CE
vertices: C, D, E
angles:
E
DE ¥ Ð D
Ð C
Ð C D Eor¥ Ð D
Ð C
¥
or¥Ð ÐE E
Ð ECDE D
D
Ð CDEC E
Ð D
¥or¥Ð ÐCC
Triangles are classified by
their sides and angles.
1)
By their angles:
a.
acute
b.
obtuse
c.
right
: three acute angles
: one obtuse Ð
: one right Ð
d. equiangular
: all Ð’s are 
Right Triangle
Acute Triangle
60°
60°
60°
Equiangular Triangle
Obtuse Triangle
2)
By their sides.
a. scalene : no sides are  ;
all different lengths.
b. isosceles
: at least 2
sides are .
c. equilateral
: all sides are 
Isosceles Triangle
Equilateral Triangle
Scalene Triangle
Theorem 3-11:
•The sum of the measures of
the angles of a triangle is 180.
2
1
3
mÐ1  mÐ2  mÐ3  180
Theorem 3-12
•The measure of an exterior
angle of a triangle equals the
sum of the measure of the
two remote interior angles
Exterior Angle
3
4
1
2
mÐ1  mÐ2  mÐ3
Corollary:
•a statement that can
be proved easily by
applying a theorem
Corollaries:
1. If two angles of one triangle are congruent to
two angles of another triangle, then the third
angles are congruent.
2. Each angle of an equiangular triangle has
measure 60.
3. In a triangle, there can be at most one right
angle or obtuse angle.
4. The acute angles of a right triangle are
complementary.