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Classifying Triangles
Angle Measures of Triangles
Triangle
• A triangle is a figure
formed by three
segments joining
three noncollinear
points.
Classifying Triangles by Sides
• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle
Equilateral Triangle
• An equilateral
triangle has three
congruent sides.
Isosceles Triangle
• An isosceles
triangle has at least
two congruent sides.
Scalene Triangle
• A scalene triangle
has no congruent
sides.
Classify the triangle by its sides.
Classification of Triangles by
Angles
•
•
•
•
Equiangular triangle
Acute triangle
Right triangle
Obtuse triangle
Equiangular Triangle
• An equiangular
triangle has three
congruent angles.
Acute Triangle
• An acute triangle
has three acute
angles.
Right Triangle
• A right triangle has
one right angle.
Obtuse Triangle
• An obtuse triangle
has one obtuse angle
Classify the triangle by its angles.
Vertex
• A vertex of a triangle
is a point that joins
two sides of the
triangle.
• The side across from
an angle is the
opposite side.
Name the side that is opposite the
angle.
• Angle J
• Angle K
• Angle L
Triangle Sum Theorem
• The sum of the measures of the angles of a
triangle is 180º.
• In ΔABC, mA + m B + m C = 180º
Find the measure of the missing angle.
Corollary to the Triangle Sum
Theorem
• The acute angles of a
right triangle are
complementary.
• In ΔABC, if m  C =
90º, then
m  A + m B= 90º
A
C
B
ΔABC is a right triangle. Find the
measure of angle A.
Interior Angles
• When the sides of a
triangle are extended,
other angles are
formed.
• The three original
angles are the
interior angles.
Exterior Angles
• The angles that are
adjacent to the
interior angles are the
exterior angles.
• It is common to show
only one exterior
angle at a vertex.
Exterior Angles Theorem
• The measure of an
exterior angle of a
triangle is equal to the
sum of the two
remote interior
angles.
• m 1 = m A + m B
Find the measure of angle 1.