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Lesson 4.1
Classifying
Triangles
Today, you will learn to…
* classify triangles by their sides and
angles
* find measures in triangles
Equilateral Triangle
3 congruent sides
Isosceles Triangle
2 congruent sides
Scalene Triangle
no congruent sides
Equiangular Triangle
3 congruent angles
Acute Triangle
70°
60°
50°
3 acute angles
Obtuse Triangle
95°
60°
25°
1 obtuse angle
Right Triangle
30°
60°
1 right angle
We classify triangles by their
sides and angles.
SIDES
Equilateral
Isosceles
Scalene
ANGLES
Equiangular
Acute
Obtuse
Right
Identify the side
opposite the
given angle.
A
C
B
CB is opposite
_____
A.
AC is opposite
_____
B.
AB is opposite
_____
C.
Leg?
leg
hypotenuse
?
leg
Leg?
leg
? base
leg
Theorem 4.1
Triangle Sum Theorem
The sum of the measures of the
interior angles of a triangle is
________
180°
1. Find m  X.
Y
mX = 44˚
61º
Z
75º
X
If the sum of the interior
angles is 180º, what
do you know about
1 and 2?
1
2
Corollary to the Triangle
Sum Theorem
The acute angles of a
right triangle are
complementary
_________________.
2. Find m F.
D
54˚ + mF = 90˚
54˚
E
mF = 36˚
F
3. Find m  1 and m  2.
50º
70º
m1 = 60˚
m2 = 120˚
exterior
angle
1 2
adjacent angles
Theorem 4.2
Exterior Angle Theorem
The measure of an exterior angle
of a triangle is equal to the sum of
the measures of the 2 nonadjacent
interior angles.
1
2
m1 + m2 = m4
3 4
m1 + m2 + m3 = 180˚
m4 + m3 = 180˚
m1 + m2 = m4
1
2
Sum of
nonadjacent
interior s
3 4
= ext. 
4. Find mE.
E
m E + 60˚ = 110˚
m E = 50˚
60˚
D
110˚
F
G
5. Find x.
E
x˚
60˚
D
x + 60 = 3x + 10
x = 25
(3x + 10)˚
F
G