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4.1 & 4.2 A Notes
CLASSIFICATION BY SIDES
Type of ∆
Equilateral
Triangle
Definition
All sides are 
Picture
CLASSIFICATION BY SIDES
Type of ∆
Isosceles
Triangle
Definition
Picture
At least 2
sides 
leg
leg
base
CLASSIFICATION BY SIDES
Type of ∆
Scalene
Triangle
Definition
No sides are 
Picture
CLASSIFICATION BY ANGLES
Type of ∆
Definition
Equiangular
Triangle
All angles are 
Picture
CLASSIFICATION BY ANGLES
Type of ∆
Acute
Triangle
Definition
All angles are
acute
Picture
CLASSIFICATION BY ANGLES
Type of ∆
Right
Triangle
Definition
Picture
leg
One right
angle
leg
CLASSIFICATION BY ANGLES
Type of ∆
Definition
Obtuse
Triangle
One obtuse
angle and 2
acute angles
Picture
Interior Angles –
Angles inside a shape
Exterior Angles –
Angles outside a shape
Corollary – Statement easily proved from
another statement
c
b
a
b
a
c
180°
The sum of the measures of a triangle = _______

If two triangles have two angles that are _______,

then the third angle is also ___________.
40°
A
B
E
80°
80°
60°
40°
C
D
60°
F
The measure of an exterior angle of a triangle is
equal to the sum of the measures of the two
remote interior angles.
a + b = 180°
b + c + d = 180°
b+c+d=a+b
c+d=a
The acute angles of a right triangle are
______________.
complementary
a + c + 90 = 180°
a + c = 90°
a
c
Classify the triangle by its sides and angles.
scalene right
Classify the triangle by its sides and angles.
equilateral
equiangular
Classify the triangle by its sides and angles.
isosceles
obtuse
4. Find the value of x. Then classify the triangle by its
angles.
2x + 3x + 55 = 180
75°
50°
5x + 55 = 180
-55 -55
5x = 125
5
5
x = 25°
acute
4. Find the value of x. Then classify the triangle by its
angles.
4x – 5 + 3x + 5 + 40 = 180
75°
65°
acute
7x + 40 = 180
-40 -40
7x = 140
7
7
x = 20°
4. Find the value of x. Then classify the triangle by its
angles.
2x + 2 + 2x + 2 + 3x + 1 = 180
52°
52°
76°
acute
7x + 5 = 180
-5 -5
7x = 175
7
7
x = 25°
5. Find the measure of each exterior angle shown.
x + 80 = 3x – 22
-x
-x
80 = 2x – 22
+22
+22
102 = 2x
2
2
51° = x
3(51) – 22 = 131°
.
5. Find the measure of each exterior angle shown.
2x + 103 – x = 6x – 7
x + 103 = 6x – 7
-x
-x
103 = 5x – 7
+7
+7
110 = 5x
5
5
22° = x
6(22) – 7 = 125°
.
5. Find the measure of each exterior angle shown.
2x + 3 + 51 = 4x + 8
2x + 54 = 4x + 8
-2x
-2x
54 = 2x + 8
46 = 2x
23° = x
4(23) + 8 = 100°
.
6. Solve for the variables.
65°
25°
y + 90 + 65 = 180
y + 155 = 180
y = 25°
6. Solve for the variables.
5y + 55 + 70 = 180
5y + 125 = 180
-125 -125
5y = 55
5
5
y = 11°
55°
7. Find the measure of each missing angle.
120°
30° 60°
60°
120°
30°
HW Problem
Section
Page #
4.1
4.2a
221
229
Assignment
1-6, 14-18, 21-26, 32, 33, 35
15, 16
Spiral ?s
1-4
4.1 # 26
Ans: 30
**Project due Tomorrow!
Bring your compass and ruler tomorrow!