4-1 Classifying Triangles

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4-1 Classifying Triangles
You measured and classified angles.

• Identify and classify triangles by angle measures.

• Identify and classify triangles by side measures.

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Definition

• A triangle is a figure formed by three line
  segments that connect three noncollinear points.

vertex
C
Side
Side
A
B
Side
vertex
vertex
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Naming a triangle

• A triangle is named using its vertices and a ?
  symbol. This triangle can be named ? ABC

C
A
B
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Classifying Triangles

• Triangles can be classified in two ways by
  their angles or by their sides.
• All triangles have at least two acute angles, but
  the third angles is used to classify the triangle.

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Triangle Classification by Angles

• Acute
• 3 acute angles
• .

Right One right angle.
Obtuse One obtuse angle.
Equiangular 3 congruent acute angles.
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A. Classify the triangle as acute, equiangular,
obtuse, or right.
Answer The triangle has three congruent angles.
It is an equiangular triangle.
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B. Classify the triangle as acute, equiangular,
obtuse, or right.
Answer One angle of the triangle measures 130,
so it is an obtuse angle. The triangle has an
obtuse angle, so it is an obtuse triangle.
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A. ARCHITECTURE The frame of this window design
is made up of many triangles. Classify ?ACD.
A. acute B. equiangular C. obtuse D. right
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Classify ?XYZ as acute, equiangular, obtuse, or
right. Explain your reasoning.
Point W is in the interior of ?XYZ, so by the
Angle Addition Postulate, m?XYW m?WYZ m?XYZ.
By substitution, m?XYZ 40 50 90.
Answer Since ?XYZ has a right angle, it is a
right triangle.
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Triangle Classification by Sides
E
B
H
A
C
G
I

• Scalene
• no sides congruent.

Equilateral All sides congruent.
D
F
Isosceles two sides congruent.
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Try ItClassify each triangle using both angle
and side classification.
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ARCHITECTURE The triangle truss shown is modeled
for steel construction. Classify ?JMN, ?JKO, and
?OLN as equilateral, isosceles, or scalene.
Answer ?JMN has no congruent sides, so it is a
scalene triangle. ?JKO has no congruent sides, so
it is a scalene triangle. ?OLN has all sides
congruent, so it is an equilateral triangle.
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ARCHITECTURE The frame of this window design is
made up of many triangles. Classify ?ABC.
A. isosceles B. equilateral C. scalene D. right
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By the definition of midpoint, VY YX.
VY YX VX Segment Addition Postulate VY
VY 8.4 Substitution 2VY 8.4 Simplify. VY 4
.2 Divide each side by 2.
So, VW 4.5 units, WY 3.0 units, and VY 4.2
units.
Answer Since all three sides have different
lengths, the triangle is scalene.
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If point C is the midpoint of , classify ?ABC
as equilateral, isosceles, or scalene.
A. equilateral B. isosceles C. scalene
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Step 1 Find d.
KM ML Given 4d 13 12 d Substitution 5d
13 12 Add d to each side. 5d 25 Add 13 to
each side. d 5 Divide each side by 5.
Step 2 Substitute to find the length of each
side. KM 4d 13 Given 5 6 or 11
d 5 4(5) 13 or 7 d 5 ML
KM Given 7 KM 7 KL d 6 Given
Answer KM ML 7, KL 11
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• What is a triangle?
• A figure formed by three line segments that
  connect three noncollinear points.
• What is the sum of the measures of the interior
  of any triangle?
• The sum of the measures of the angles of a
  triangle is 180
• How are triangles classified and named?
• Triangles are classified by sides and angles.
• Sides scalene, isosceles and equilateral.
• Angles acute, obtuse, right and equiangular.

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4-1 Assignment

• Page 240, 15 -20, 22-36 even, 40 - 42