CLASSIFYING TRIANGLES BY ANGLES. Classifying Triangles by Angles ACUTE OBTUSE RIGHT EQUIANGULAR.
4.1 Triangles & Angles
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Transcript of 4.1 Triangles & Angles
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A Triangle
• Is a figure formed by three segments
• Joining three noncollinear points….it has
• Sides…..
• And Angles.
ABC
C
B
A
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Triangles can be classified by sides..
• Scalene (no sides equal)
• Isosceles (as least 2 sides equal)
• Equilateral (3 congruent sides) JKL
DEF
ABC
L
KJ
F
ED
C
B
A
A
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A Triangle can be classified by ANGLES…
• Acute (3 acute angles)
• Right (1 right angle)
• Obtuse (1 obtuse angle)
• Equiangular (3 congruent angles)
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Triangle Vocabulary
• Vertex A
• Vertex B
• Vertex C
C
AB
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Triangle Vocabulary
• Side opposite angle A
• Side opposite angle B
• Side opposite angle C
C
AB
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Right Triangles
• Hypotenuse
• Leg
• Leg
C
AB
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Isosceles Triangle
• Base
• Leg
• Leg
C
A
B
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When the sides of a triangle are extended….the triangle has
• Interior Angles
• Exterior AnglesExteriorAngle
ExteriorAngle
ExteriorAngle
InteriorAngles
C
A
B
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Classify the triangle by it’s SIDES and Angles.
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Classify the triangle by it’s SIDES and Angles.
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Classify the triangle by it’s SIDES and Angles.
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Classify the triangle by it’s SIDES and Angles.
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Classify the triangle by it’s SIDES and Angles.
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Classify the triangle by it’s SIDES and Angles.
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Complete each sentence with the word always, sometimes or
never.
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Click here to explore
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Click here to explore
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Theorem 4.1-Triangle Sum Theorem
• The sum of the interior angles of a triangle is 180 degrees.
mABC+mDEF+mGHI = 180
mGHI = 42mDEF = 32mABC = 106
B
E
A
C
GI
D
F
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What is the measure of the numbered angle?
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What is the measure of the numbered angle?
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What is the measure of the numbered angle?
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Theorem 4.2-Exterior Angle Theorem
• The measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles.
mDEF+mGHI = 142
mGHI = 73
mDEF = 68
mCBA = 142
E
H
BG
I
FD
CA
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A corollary to a theorem
• Is a statement that can be proved easily using a theorem
• Think of it as a mini-theorem.
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Corollary to the triangle sum theorem
• The acute angles of a right triangle are complementary. C
BA
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Assignment 4.1