Download 4.1 Classifying Triangles Sides Angles

December 13, 2012
4.1 Classifying Triangles
Sides
Angles
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4.2 Angle Relationships in Triangles
Theorem:
The sum of the interior angles of a triangle is 180
A
m A + m B + m C = 180
C
B
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Proof of Triangle Sum Theorem
Given: AD II BC
Prove: m 1 + m 2 + m 3 = 180
Statement
Reason
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1.
60
70
55
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2.
corollary: The measure of each angle of an equiangular triangle is 60o.
Corollary: a theorem in which the proof follows directly from
another theorem.
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Find x.
3.
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Corollary:
The acute angles of a right triangle are complementary.
Proof:
Given:
Prove:
ABC is right with rt
A comp. C
Statements
B
Reasons
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4
5
6
interior angles:
1,
2,
3
exterior angles:
4,
5,
6
remote interior: interior angle that is not
adjacent to the exterior angle.
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80
60
x
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Exterior Angle Theorem:
The measure of an exterior angle of a triangle is equal to
the sum of its 2 remote interior angles.
B
A
2
Proof
Given:
Prove:
Statement
ABC
m 1=m B+m A
Reason
1
C
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Examples. Find x.
1.
2.
80
x
3.
3x-22
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E
C
D
A
F
B
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Third Angles Theorem:
If 2 angles of one triangle are congruent to 2 angles
of another triangle, then the third angles are congruent.
4y2
6y2-40
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E
C
A
D
Given:
C = E
D = F
Prove:
A = B
Statements
F
Reasons
B
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Examples.
1. The measure of one acute angle of a right triangle is one-fourth the
measure of the other acute angle. Find the angles.
2. The ratio of the measures of a triangle are 3:2:1. Find the measure of each
angle.