Triangles

1
Triangles

• Section 2-1

Key Terms Exterior Angle, Remote Interior Angles,
Corollary, Equilateral, Isosceles, Scalene,
Equiangular
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The triangle angle sum theoremTheorem 2-1

• The sum of the measures of the angles of a
  triangle is 180.
• mltA mltB mltC 180

A
C
B
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Exterior Angles of Triangle

• Exterior Angle
• The angle formed by a side and an extension of
  the side
• Remote Interior Angle
• The two non-adjacent interior angles

Remote Interior Angles
Exterior Angle
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Exterior Angle TheoremTheorem 2-2

• The measure of each exterior angle of a triangle
  equals the sum of the measures of its two remote
  interior angles.
• mlt1 mlt2 mlt3

2
3
1
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Corollary to Theorem 2-2

• The measure of an exterior angle of a triangle is
  greater than the measure of either of its remote
  interior angles.
• mlt1 gt mlt2 AND mlt1 gt mlt3

2
3
1
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Types of Trianglesby Sides

• Equilateral
• All sides congruent
• Isosceles
• At least two sides are congruent
• Scalene
• No sides are congruent

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Types of Trianglesby Angles

• Equiangular
• All angles are congruent
• Acute
• All angles are acute (less than 90)
• Right
• One right angle (90 )
• Obtuse
• One obtuse angle (more than 90 less than 180)

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Examples