4.1 Triangle Sum Conjecture
Investigation:
Step 1 Measure the angles of each triangle as accurately as possible with your protractor.
Step 2 Find the sum of the measures of the three angles in each triangle. Compare results with others
in your group. Does everyone get the same result? What is it?
Step 3 Check the sum another way. Carefully cut out one triangle, write the letters a, b, and c in the
interiors of the three angles.
Step 4 Tear off the three angles.
Step 5 Arrange the three angles so that their vertices meet at a point. How does this arrangement
show the sum of the angle measures? Compare results with others in your group. State a
conjecture.
Geometry Lesson 4.1: Triangle Sum Conjecture
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Investigation Worksheet
Geometry Lesson 4.1: Triangle Sum Conjecture
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Triangle Sum Conjecture
The sum of the measures of the angles of every triangle is _______.
B
A
C
mA + mB + mC = ___________
Third Angle Conjecture
If two angles of one triangle are equal in measure to two angles of another triangle, then the
___________ angles in each triangle are equal in measure.
E
B
A
D
C
F
If mA = mD and mB = mE, then mC = mF
Geometry Lesson 4.1: Triangle Sum Conjecture
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Example 1: Find each missing angle measure.
B
F
D
41
140
39
A
E
C
mB = _________
mD = _________
mF = _________
H
N
J
73
K
I
78
G
132
115
L
mH = _________
mJ = _________
mI = _________
mGKJ = _________
Geometry Lesson 4.1: Triangle Sum Conjecture
M
mNLM = _________
mNML= _________
mLNM = _________
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Example 2: Find the values of x, y, and z.
27
34
26
66
x
x = _________
y
28
z
60
y = _________
x
x = _________
z = _________
y
z
y = _________
z = _________
Example 3: Find the values of x and y.
x
x
55
50
59
47
55
59
y
y
x = _________
y = _________
Geometry Lesson 4.1: Triangle Sum Conjecture
x = _________
y = _________
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Example 4: Find each missing angle measure.
76
60
84
a
n
b
m
e
k
52
d
j
c
51
i
38
f
g
h
45
84
a = _______
b = _______
c = _______
d = _______
e = ______
f = _______
g = _______
h = _______
i = _______
j = ______
k = _______
m = _______
n = _______
Homework: pp. 201 – 203 => 2 – 9; 22
Geometry Lesson 4.1: Triangle Sum Conjecture
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