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Geometry Theorems for Triangles Application

This Warm Up Answer explains how to apply theorems about interior angles, exterior angles, and midlines of triangles, proving the sum of triangle angles is 180. The text covers various theorems and proofs related to triangle properties.

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Geometry Theorems for Triangles Application

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  1. Warm Up

  2. Answer

  3. 7.1- Triangle Application Theorems Objective- apply theorems about interior angles, the exterior angles and the midlines of triangles

  4. T50- the sum of the measures of the angles of a triangle is 180

  5. Given: triangle ABC Prove m<A+ m<B +m<C = 180*

  6. 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… <1 + <2 + <3 = 180 (straight line) <1= <C alt. int. <s <3=<B alt. int. <s So m<A +m<B+ m<C= 180

  7. 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

  8. 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.

  9. Proof of Theorem 51 m<BCA +m<1 = 180 m<BCA + m <B + m<A = 180 m <BCA + m <1 = m <BCA + m <B +m <A m <1 = m <B + m <A

  10. Proof for Theorem 52 P

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