Classifying Triangles

1
Naming Triangles
Triangles are named by using its vertices.
For example, we can call the following triangle
?ABC
?BAC
?ACB
?CAB
?BCA
?CBA
2
Opposite Sides and Angles
Opposite Sides
Side opposite to ?A
Side opposite to ?B
Side opposite to ?C
Opposite Angles
Angle opposite to ?A
Angle opposite to ?B
Angle opposite to ?C
3
Classifying Triangles by Sides
Scalene
A triangle in which all 3 sides are different
lengths.
AB 3.47 cm
AC 3.47 cm
AB 3.02 cm
AC 3.15 cm
Isosceles
A triangle in which at least 2 sides are equal.

• Equilateral

A triangle in which all 3 sides are equal.
GI 3.70 cm
GH 3.70 cm
4
Classifying Triangles by Angles
Acute

• A triangle in which all 3 angles are less than
  90.

Obtuse
A triangle in which one and only one angle is
greater than 90 less than 180
5
Classifying Triangles by Angles
Right
A triangle in which one and only one angle is 90
Equiangular
A triangle in which all 3 angles are the same
measure.
6
Classification by Sides with Flow Charts Venn
Diagrams
Polygon
Triangle
Scalene
Isosceles
Equilateral
7
Classification by Angles with Flow Charts Venn
Diagrams
Polygon
Triangle
Right
Acute
Obtuse
Equiangular
8
Theorems Corollaries
The sum of the interior angles in a triangle is
180.
Triangle Sum Theorem
Third Angle Theorem
If two angles of one triangle are congruent to
two angles of a second triangle, then the third
angles of the triangles are congruent.
Corollary 1
Each angle in an equiangular triangle is 60.
Corollary 2
Acute angles in a right triangle are
complementary.
There can be at most one right or obtuse angle in
a triangle.
Corollary 3
9
Exterior Angle Theorem
The measure of the exterior angle of a triangle
is equal to the sum of the measures of the remote
interior angles.
Remote Interior Angles
A
Exterior Angle
D
B
Example
Find the m?A.
C
3x - 22 x 80 3x x 80 22 2x 102
m?A x 51
10
Median - Special Segment of Triangle
Definition
A segment from the vertex of the triangle to the
midpoint of the opposite side.
Since there are three vertices, there are three
medians.
In the figure C, E and F are the midpoints of the
sides of the triangle.
11
Altitude - Special Segment of Triangle
The perpendicular segment from a vertex of the
triangle to the segment that contains the
opposite side.
Definition
In a right triangle, two of the altitudes are the
legs of the triangle.
In an obtuse triangle, two of the altitudes are
outside of the triangle.
12
Perpendicular Bisector Special Segment of a
triangle
A line (or ray or segment) that is perpendicular
to a segment at its midpoint.
Definition
The perpendicular bisector does not have to start
from a vertex!
Example
A
E
A
B
In the isosceles ?POQ, is the
perpendicular bisector.
B
In the scalene ?CDE, is the
perpendicular bisector.
In the right ?MLN, is the perpendicular
bisector.