Geometry

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Geometry

• Notes Section 4-2

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What youll learn. . . .

• How to apply the angle sum theorem
• How to recognize exterior angles and apply the
  exterior angle theorem

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Vocabulary

• Exterior angle of a triangle
• Remote interior angles
• Third angle theorem

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The Angle Sum Theorem
Consider the sum of the angles of a triangle. . .
.

• The sum of the measures of the angles of a
  triangle will always be 180

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Example 1Determine the angle measures.
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Example 2Determine the angle measures.
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Example 3Determine the angle measures
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Example 4Determine the angle measure

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The Exterior Angle Theorem
2
4
1
3
Exterior Angles will always make a linear pair
with an interior angle of a triangle.

• Each exterior angle will be associated with 2
  remote interior angles (the two angles not
  connected to that exterior angle).

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The exterior angle theorem
Exterior angles and their remote interior angles
share a special relationship.

• The measure of an exterior angle of a triangle
  will always be equal to the sum of the measures
  of its remote interior angles.

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Example Problem 5

• Find x and y.

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The Third angle Theorem
2
4
1
5
3
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If two angles of one triangle measure the same as
two angles from another triangle, their third
angles must also be the same measure.
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Example Problem 6

• Find x and y.

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Have you learned. . . .

• How to apply the angle sum theorem
• How to recognize exterior angles and apply the
  exterior angle theorem

• Assignment
• Non-Proof Worksheet 4-2
• Proof p.189 (15-38) all diagrams must be drawn
  in your homework