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Math 2 Geometry
Based on Elementary Geometry, 3rd ed, by Alexander & Koeberlein
2.4
The Angles of a Triangle
Definition
A triangle is the union of three line
segments that are determined by three
non-collinear points.
Definition
A triangle is the union of three line
segments that are determined by three
non-collinear points.
A•
•B
•C
Definition
A triangle is the union of three line
segments that are determined by three
non-collinear points.
A•
•B
•C
Definition
A triangle is the union of three line
segments that are determined by three
non-collinear points.
A•
•B
•C
ABC
Informal Definitions
Each point A, B, C is a vertex. (pl. Vertices)
Segments AB, BC, and CB are sides.
Point D is in the interior of the triangle.
Point E is in the exterior of the triangle.
A•
•B
•C
Triangles classified by sides
• Scalene
No congruent sides
• Isosceles
At least two  sides
• Equilateral
Three  sides
Triangles classified by angles
• Acute
All angles acute
• Obtuse
One obtuse angle
• Right
One right angle
• Equiangular
All angles 
Theorem 2.4.1
In a triangle, the sum of the measure of
the interior angle is 180.
What is
an interior
angle?
A•
•B
•C
We can prove this theorem
If the sum of the measures of the interior
angles of a triangle is 180…
… what can we say about the angles in an
equiangular triangle?
Corollary 2.4.1
Each angle of an equiangular triangle
measures 60
If the sum of the measures of the interior
angles of a triangle is 180…
… what can we say about the angles in a
right triangle?
A
C
B
Corollary 2.4.3
The acute angles of a right triangle are
complementary.
A
Are the two non-right
angles really acute? C
mA + mB + mC=180
B
Corollary 2.4.4
If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are also congruent.
Corollary 2.4.4
If two angles of one triangle are congruent to two
angles of another triangle, then the third angles
are also congruent.
Notice that this does not mean the two
triangles are necessarily congruent.
Corollary 2.4.5
The measure of an exterior angle of a
triangle equals the sum of the measures of
the two non-adjacent interior angles.
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