Angles of a Triangle

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 angle
s or
or or
C, D, E
4
Triangles are classified by their sides and
angles.
1) By their angles

5
Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle
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2) By their sides.
a. scalene no sides are ? all
different lengths.
b. isosceles at least 2
sides are ?.
c. equilateral all sides are ?
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Isosceles Triangle
Equilateral Triangle
Scalene Triangle
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Theorem 3-11

• The sum of the measures of the angles of a
  triangle is 180.

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Theorem 3-12

• The measure of an exterior angle of a triangle
  equals the sum of the measure of the two remote
  interior angles

10
3
4
1
2
11
Corollary

• a statement that can be proved easily by applying
  a theorem

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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.