Math 109

Section 2.4

Definition: A triangle is the union of three line segments that are determined by three non-collinear points.

A triangle has three vertices.

All points that lie inside the triangle are considered to be in the interior of the triangle.

All points that lie outside the triangle are considered to be in the interior of the triangle

Classification of Triangles

Type of Triangle	Drawing	Number of Congruent Sides
Scalene		None
Isosceles		Two
Equilateral		Three

Triangles Classified by Angle

Triangle	Types of Angles
Acute	All acute angles
Obtuse	One obtuse angles
Right	One right angle
Equiangular	All angles are congruent

Theorem 2.4.1: The sum of the interior angles of a triangle is 180º

Corollary 2.4.2: Each angle of an equilateral triangle measures 60º

Corollary 2.4.3: The acute angles of a right triangle are complementary.

Corollary 2.4.4: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent.

C

A B

D

E F

Corollary 2.4.5: The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles.

Page 93

Figure 2.4.1

Use for 2 and 4

2)

4)

Classify the triangle by considering the lengths of sides.

6)

a)

b)

Classify the triangle by consider the measures of each interior angle.

8)

a)

b)

12)

16)

20)

22)