4.1 & 4.2 A Notes
4.1 & 4.2 A Notes. Type of ∆DefinitionPicture Equilateral Triangle CLASSIFICATION BY SIDES All sides are
Jan 18, 2016
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4.1 & 4.2 A Notes
Type of ∆ Definition Picture
Equilateral Triangle
CL
AS
SIF
ICA
TIO
N B
Y S
IDE
S
All sides are
Type of ∆ Definition Picture
Isosceles Triangle
CL
AS
SIF
ICA
TIO
N B
Y S
IDE
S
At least 2 sides
base
leg leg
Type of ∆ Definition Picture
Scalene Triangle
CL
AS
SIF
ICA
TIO
N B
Y S
IDE
S
No sides are
Type of ∆ Definition Picture
EquiangularTriangle
CL
AS
SIF
ICA
TIO
N B
Y A
NG
LE
S
All angles are
Type of ∆ Definition Picture
Acute Triangle
CL
AS
SIF
ICA
TIO
N B
Y A
NG
LE
S
All angles are acute
Type of ∆ Definition Picture
Right Triangle
CL
AS
SIF
ICA
TIO
N B
Y A
NG
LE
S
One right angle leg
leghyp
oten
use
Type of ∆ Definition Picture
Obtuse Triangle
CL
AS
SIF
ICA
TIO
N B
Y A
NG
LE
S
One obtuse angle and 2 acute angles
Interior Angles – Angles inside a shape
Exterior Angles – Angles outside a shape
Corollary – Statement easily proved from another statement
a c
b
ac b
The sum of the measures of a triangle = _______180°
If two triangles have two angles that are _______,
then the third angle is also ___________.
A
B
C D
E
F
40° 40°60° 60°
80° 80°
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
a + c + 90 = 180°a + c = 90°
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
5x + 55 = 180 -55 -55
5x = 125
x = 25°5 5
50°
75°
acute
4. Find the value of x. Then classify the triangle by its angles.
4x – 5 + 3x + 5 + 40 = 180
7x + 40 = 180 -40 -40
7x = 140
x = 20°7 7
75°
65°
acute
4. Find the value of x. Then classify the triangle by its angles.
2x + 2 + 2x + 2 + 3x + 1 = 180
7x + 5 = 180 -5 -5
7x = 175
x = 25°7 7
52°52°
76°
acute
5. Find the measure of each exterior angle shown.
x + 80 = 3x – 22 -x -x .
102 = 2x
51° = x
2 2
80 = 2x – 22 +22 +22
3(51) – 22 = 131°
5. Find the measure of each exterior angle shown.
2x + 103 – x = 6x – 7
-x -x .
110 = 5x
22° = x5 5
103 = 5x – 7 +7 +7
x + 103 = 6x – 7
6(22) – 7 = 125°
5. Find the measure of each exterior angle shown.
2x + 3 + 51 = 4x + 8
-2x -2x .
46 = 2x23° = x
54 = 2x + 8
2x + 54 = 4x + 8
4(23) + 8 = 100°
6. Solve for the variables.
65°
y + 90 + 65 = 180
y = 25°
25°
y + 155 = 180
6. Solve for the variables.
55°
5y + 55 + 70 = 180
5y + 125 = 180 -125 -125
5y = 55
y = 11°5 5
7. Find the measure of each missing angle.
120°
120°60°30°
60°
30°
Ans: 30
**Project due Tomorrow! Bring your compass and ruler tomorrow!
HW ProblemSectio
nPage # Assignment Spiral ?
s
4.14.2a
221229
1-6, 14-18, 21-26, 32, 33, 3515, 16
1-4
4.1 # 26
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