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1)
30 + 90 + X = 180
2)
55 + X + 105 = 180
3)
X + 58 = 90
4)
31 + X = 90
Triangles, Triangles,
and MORE Triangles
Geometry
Week 7 of 9
Unit 2: Angles and Angle Relationships
10/1 & 10/2
Standards & Objectives
Standard 12.0 and 13.0
Objectives:
To classify triangles and find the measures of their
angles
To use exterior angles of triangles
ACTIVITY
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Draw and cut out a large triangle.
Number the angles and tear them off.
Place the three angles adjacent to each other to
form one angle.
1) What kind of angle is formed by the three
smaller angles? What is its measure?
2) Make a conjecture about the sum of the
measures of the angles of a triangle.
Triangle Angle-Sum Theorem

The sum of the measures of the angles of a
triangle is 180.
Different Types of Triangles
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There are several different types of triangles.
You can classify a triangle by its sides and its
angles.
There are THREE different classifications for
triangles based on their sides.
There are FOUR different classifications for
triangles based on their angles.
Classifying Triangles by Their Sides

EQUILATERAL – 3 congruent sides

ISOSCELES – at least two sides
congruent

SCALENE – no sides congruent
Classifying Triangles by Their
Angles

EQUIANGULAR – all angles are congruent

ACUTE – all angles are acute
EQUIANGULAR

RIGHT – one right angle
ACUTE
RIGHT

OBTUSE – one obtuse angle
OBTUSE
Can You Classify the Different
Triangles in the Picture Below?
Classify the following triangles: AED, ABC, ACD, ACE
The Classifications…

Triangle AED = Equilateral, Equiangular
Triangle ABC = Equilateral, Equiangular
Triangle ACD = Scalene, Obtuse
Triangle ACE = Scalene, Right
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So how did you do?
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Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle
equals the sum of the measures of its two
remote interior angles.
2
1
3
EXAMPLE
40
30
X
Measure of X = 40 + 30
Measure of X = 70
PRACTICE
EXAMPLE
X
113
113 = 70 + Measure of X
43 = Measure of X
70