Definition
Math 2 Geometry
Based on Elementary Geometry, 3rd ed, by Alexander & Koeberlein
A triangle is the union of three line
segments that are determined by three
non-collinear points.
2.4
The Angles of a Triangle
•B
A•
•C
Definition
Informal Definitions
A triangle is the union of three line
segments that are determined by three
non-collinear points.
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.
•B
•B
A•
A•
•C
Triangles classified by sides
• Scalene
• Isosceles
• Equilateral
•C
UABC
No congruent sides
Triangles classified by angles
• Acute
All angles acute
• Obtuse
One obtuse angle
• Right
One right angle
• Equiangular
All angles ≅
At least two ≅ sides
Three ≅ sides
1
Theorem 2.4.1
In a triangle, the sum of the measure of
the interior angle is 180°.
If the sum of the measures of the interior
angles of a triangle is 180°…
•B
What is
an interior
angle?
A•
… what can we say about the angles in an
equiangular triangle?
•C
We can prove this theorem
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
Corollary 2.4.3
Corollary 2.4.4
The acute angles of a right triangle are
complementary.
If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are also congruent.
A
Are the two non-right
angles really acute? C
B
B
m∠A + m∠B + m∠C=180
2
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 2.4.5
The measure of an exterior angle of a
triangle equals the sum of the measures of
the two non-adjacent interior angles.
Notice that this does not mean the two
triangles are necessarily congruent.
2
1
3
4
3