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4.1 Classifying Triangles
Objectives
 Identify and classify triangles by angles
 Identify and classify triangles by sides
Parts of a Triangle
 A triangle is a 3-sided polygon
 The sides of ∆ABC are




AB, BC, and AC
The vertices of ∆ABC are
A, B, and C
Two sides sharing a common
vertex are adjacent sides
The third side is called the
opposite side
All sides can be adjacent or
opposite (it just depends which
vertex is being used)
A
adjacent
adjacent
B
Side
opposite
A
C
Classifying Triangles by Angles
One way to classify triangles is
by their angles…
Acute
Obtuse
all 3 angles are acute 1 angle is obtuse
(measure < 90°)
(measure > 90°)
Right
1 angle is right
(measure = 90°)
An acute ∆ with all angles  is an equiangular ∆ .
Example 1:
ARCHITECTURE The triangular truss below is
modeled for steel construction. Classify
JMN, JKO, and OLN as acute, equiangular, obtuse,
or right.
Example 1:
Answer:
JMN has one angle with measure greater than 90, so it
is an obtuse triangle.
JKO has one angle with measure equal to 90, so it is a
right triangle.
OLN is an acute triangle with all angles congruent, so it
is an equiangular triangle.
Classifying Triangles by Sides
Another way to classify triangles
is by their sides…
Equilateral
3 congruent sides
Isosceles
2 or more
congruent sides
Scalene
no congruent sides
Example 2a:
Identify the isosceles triangles in the figure if
Isosceles triangles have at least two sides congruent.
Answer: UTX and UVX are isosceles.
Example 2b:
Identify the scalene triangles in the figure if
Scalene triangles have no congruent sides.
Answer: VYX, ZTX, VZU, YTU, VWX,
ZUX, and YXU are scalene.
Example 2c:
Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD
Example 3:
ALGEBRA Find d and the measure of each side of
equilateral triangle KLM if
and
Since KLM is equilateral,
each side has the same
length. So
5=d
Example 3:
Next, substitute to find the length of each side.
KL = 7
LM = 7
KM = 7
Answer: For KLM,
and the measure of
each side is 7.
Your Turn:
ALGEBRA Find x and the measure of each side of
equilateral triangle
if
and
Answer:
Example 4:
COORDINATE GEOMETRY Find the measures of the
sides of RST. Classify the triangle by sides.
Example 4:
Use the distance formula to find the lengths of each side.
Answer:
; since all 3 sides
have different lengths, RST is scalene.
Assignment
 Geometry:
Pg. 181 #13 – 18, 22 – 28, 32, 34
 Pre-AP Geometry:
Pg. 181 #13 – 18, 22 – 29, 32, 34, 36, 38