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  Chapter 4.CR, Problem 23CR
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  ### Elementary Geometry For College St...
  
  7th Edition
  Alexander + 2 others
  ISBN: 9781337614085
  
  #### Solutions
  
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  ### Elementary Geometry For College St...
  
  7th Edition
  Alexander + 2 others
  ISBN: 9781337614085
  Textbook Problem
  
  # Review ExercisesIn Review Exercises 22 to 24, M and N are the midpoints of F J - and F H - respectively. Given: J H = 12 m ∠ J = 80 ° m ∠ F = 60 ° Prove: M N ,   m ∠ F M N ,   m ∠ F N M
  
  To determine
  
  To Find:
  
  The length of the line joining the mid points of the sides of the triangle and measure of angles based on the information provided.
  
  Explanation
  
  Formula Used:
  
  Sum of the interior angle of a triangle is 180Â°.
  
  Theorem on triangle:
  
  The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.
  
  That is, âˆ†ABC with midpoints M and N of AB- and AC-, respectively. Then MN-âˆ¥BC-. It can be concluded that BC=12(MN)
  
  Calculation:
  
  It is given that âˆ†FJH is an isosceles triangle with M and N are the midpoints of FJ- and FH- respectively.
  
  Also given that JH=12, mâˆ J=80Â° and mâˆ F=60Â°.
  
  Applying the theorem, MN is parallel to JH.
  
  So mâˆ FHJ=mâˆ FNM and mâˆ FJH=mâˆ FMN.
  
  Here mâˆ J=80Â°
  
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