4'2 Angles of Triangles 111108

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4.2 Angles of Triangles 11/11/08

• Angle Sum Theorem
• The sum of the measures of angles of a triangle
  is 180.

X
W
Y
m W m X m Y 180
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Interior Angles

• Find the missing angle measures.

82
28
1
2
68
3
3
Interior Angles

• It is easiest to find the measure of angle 1
  first.
• Now, find angles 2 and 3.
• Angle 2 is a congruent vertical angle with angle
  1.

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Third Angle Theorem

• If two angles in one triangle are congruent to
  two angles of a second triangle, then the third
  angles of the triangles are congruent.
• If angle A is congruent to angle F, and angle C
  is congruent to angle D, then angle B is
  congruent to angle E.

C
F
A
B
D
E
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Exterior Angles

• An exterior angle is formed by one side of a
  triangle and the extension of another side.
• The interior angles of the triangle not on
  adjacent to the given exterior angle are called
  remote interior angles of the exterior angle.

2
Remote Interior Angles
Exterior Angle
1
3
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Exterior Angles Theorem

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

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Exterior Angles

• Find the measure of each numbered angle.

3
2
50
1
120
5
4
56
78
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Corollaries

• A corollary a statement that can be easily
  proved using a theorem.
• Corollary 4.1
• The acute angles of a right triangle are
  complementary.
• Corollary 4.2
• There can be at most one right or obtuse angle in
  a triangle.

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Homework