4-1 Triangles and Angles

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4-1 Triangles and Angles
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Theorem 4.1 Triangle Sum

• The sum of the measures of the interior angles of
  a triangle is 180?.

x y z 180?
y?
x?
z?
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Theorem 4.2 Exterior Angle

• The measure of an exterior angle of a triangle is
  equal to the sum of the measures of the two
  nonadjacent (remote) interior angles.

m?4 m?1 m?2
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4
1
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Triangle Sum Corollary

• The acute angle of a right triangle are
  complementary.

a b 90?
a?
b?
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Classifying Triangles by Sides

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

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Classifying Triangles by Angles

• Equiangular Triangle
• All angles are congruent.
• Right Triangle
• One angle is a right angle.
• Obtuse Triangle
• One angle is an obtuse angle.
• Acute Triangle
• All angles are acute angles.

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Right Triangles
B
hypotenuse
leg
C
leg
A
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Isosceles Triangles
leg
leg
base
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Find the measure of the exterior angle.
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