Theorem 18-1 Triangle Angle Sum Theorem

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Theorem 18-1Triangle Angle Sum Theorem

• The sum of the measures of the angles of a
  triangle is equal to 180o

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Corollary

• A corollary to a theorem is a statement that
  follows directly from that theorem

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TRIANGLE ANGLE SUM THEOREM COROLLARIES

• Corollary 18-1-1 If 2 angles of 1 triangle are
  congruent to 2 angles of another triangle, then
  the 3rd angles are congruent
• Corollary 18-1-2 The acute angles of a right
  triangle are complementary
• Corollary 18-1-3 The measure of each angle of an
  equiangular triangle is 60o
• Corollary 18-1-4 A triangle can have at most 1
  right or 1 obtuse angle

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Finding angle measures in right triangles

• Find ltD in triangle DEF .
• Use corollary 18-1-2

D
E
58o
F
5

• In right triangle KLM,
• ltK is congruent to ltL, Find mltK
• Use corollary 18-1-4

L
M
K
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REMOTE INTERIOR ANGLE

• In any polygon, a remote interior angle is an
  interior angle that is not adjacent to a given
  exterior angle A and B are remote to angle 1

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Theorem 18-2Exterior Angle Theorem

• The measure of each exterior angle of a triangle
  is equal to the sum of the measures of its 2
  remote interior angles.
• MltDCA mltA mltB

A
B
C
D
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Using Exterior angle theorem

• Determine the measure of ltWYZ,
• If lt3 50, ltX 70

Z
W
X
Y