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  Chapter 4.CR, Problem 23CR
  BuyFindarrow_forward
  
  ### Elementary Geometry For College St...
  
  7th Edition
  Alexander + 2 others
  ISBN: 9781337614085
  
  #### Solutions
  
  Chapter
  Section
  BuyFindarrow_forward
  
  ### 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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  #### True or False: If f(x) = F(x), then baf(x)dx=F(b)F(a).
  
  Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
explanation: The provided text is an excerpt from a geometry textbook problem and solution. It describes a geometry problem involving an isosceles triangle FJH with midpoints M and N on sides FJ and FH, respectively. The problem provides the length of JH and the measures of angles J and F, and asks to prove the length of MN and the measures of angles FMN and FNM.
  
  The text also includes a partial solution, explaining that MN is parallel to JH and that the angles FHJ and FNM, as well as FJH and FMN, are equal. It then states that the measure of angle J is 80°.
  
  However, the text does not provide a complete answer to the problem, as it cuts off before completing the proof.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: menu
  Hit Return to see all results
  Chapter 4.CR, Problem 23CR
  BuyFindarrow_forward
  
  ### Elementary Geometry For College St...
  
  7th Edition
  Alexander + 2 others
  ISBN: 9781337614085
  
  #### Solutions
  
  Chapter
  Section
  BuyFindarrow_forward
  
  ### 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°
  
  ### Still sussing out bartleby?
  
  Check out a sample textbook solution.
  
  See a sample solution
  
  #### The Solution to Your Study Problems
  
  Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!
  
  Get Started
  
  ## Additional Math Solutions
  
  #### Find more solutions based on key concepts
  
  Show solutions add
  
  #### True or False: If f(x) = F(x), then baf(x)dx=F(b)F(a).
  
  Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an excerpt from a geometry textbook problem and solution. It describes a geometry problem involving an isosceles triangle FJH with midpoints M and N on sides FJ and FH, respectively. The problem provides the length of JH and the measures of angles J and F, and asks to prove the length of MN and the measures of angles FMN and FNM.
  
  The text also includes a partial solution, explaining that MN is parallel to JH and that the angles FHJ and FNM, as well as FJH and FMN, are equal. It then states that the measure of angle J is 80°.
  
  However, the text does not provide a complete answer to the problem, as it cuts off before completing the proof.
  
  Label: question-and-answer (partial)