Chapter 3.5 The Triangle Sum Theorem

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Chapter 3.5The Triangle Sum Theorem

• Created by
• Claudia, Chris, Brittany, and Shannon

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The Parallel Postulate

• Given a line and a point not on the line, there
  is one and only one line that contains the given
  point and is parallel to the given line.
• Ex.

P
P
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The Triangle Sum Theorem

• The sum of the measures of the angles of a
  triangle are equal to 180 degrees.

lt 5 lt 3 and lt 4 lt 1 because alternate interior
angles are congruent. Since lt1 lt 2 lt 3180
degrees then the sum of the interior angles is
180.
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Example!
lt 1 lt 4 because of alternate interior angles and
lt 3 lt 5 . The sum of lt 1 lt 3 130 so lt 2 would
equal 50. ( 180- 130 50). The sum of angles
2,4, and 5 180 because lt 250 and lt 4 50.
This proves the triangle sum theorem.
50
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3
2
80
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Definition of Remote Interior Angles

• An Interior angle of a triangle that is not
  adjacent to a given exterior angle.
• Ex.

Angles 1 and 2 are remote Interior angles of
angle 4.
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Exterior Angle Theorem

• The Exterior Angle equals the sum of the two
  remote interior angles. (remote interior angles
  dont touch the exterior angle).

lt 4 equals the sum of lt1 lt2 . 5070 120 so lt4
120
50
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70
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How to find the measure of the interior angles of
a convex polygon

• You start from one point and the polygon and use
  only that point. You draw a line from that
  endpoint to all the other endpoint possible and
  see how many triangles you make. Then you take
  the number of triangles and multiply it by 180 to
  get the measure of the interior angles of that
  polygon.

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Ex.
Starting point
You can make 4 triangles with a hexagon so the
measure of the interior angles would equal 720.
(4180720).
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The End!