Warm Up

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Warm Up
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Answer
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7.1- Triangle Application Theorems

• Objective- apply theorems about interior angles,
  the exterior angles and the midlines of triangles

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• T50- the sum of the measures of the angles of a
  triangle is 180

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• Given triangle ABC
• Prove mltA mltB mltC 180

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• Proof
• According to the Parallel Postulate , these
  exists exactly one line through point A parallel
  to BC so the figure at the right can be drawn

lt1 lt2 lt3 180 (straight line) lt1 ltC alt.
int. lts lt3ltB alt. int. lts So mltA mltB mltC 180
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• Exterior angles of a polygon
• Definition- an exterior angle of a polygon is an
  angle that is adjacent to and supplementary to an
  interior angle of the polygon

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• More Theorems!
• (please applaud now!)
• T51- triangles only the measure of an exterior
  angle of a triangle is equal to the sum of the
  measures of the remote interior angles
• T52- A segment joining the midpoints of two
  sides of a triangle is parallel to the third side
  and its length is 1/2 the length of the third
  side.

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• Proof of Theorem 51
• mltBCA mlt1 180
• mltBCA m ltB mltA 180
• m ltBCA m lt1 m ltBCA m ltB m ltA
• m lt1 m ltB m ltA

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Proof for Theorem 52
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