SOLUTION: given that DEFG ia a parallelogram and h is where segment DF and segment EG intersect. prove that measurement of angle DHG=measurement of angle EDH and measurement of angle FGH

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Question 178996This question is from textbook Homework and Practice Workbook
: given that DEFG ia a parallelogram and h is where segment DF and segment EG intersect.
prove that measurement of angle DHG=measurement of angle EDH and measurement of angle FGH This question is from textbook Homework and Practice Workbook

Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
@ represents angle
:

::
*************************************************************************
           statement                            reason
*************************************************************************
1.DEFG is a parallelogram                    1.Given
  H is where segment DF and EG intersect

2.@EDH+@HDG+@HGD+@FGH=180                    2.def of parallelogram-consecutive
                                               angles are supplementary

3.     @HDG+@HGD+@DHG=180                    3.def of a triangle

4.     @HDG+@HGD=180-@DHG                    4.subtraction post.

5.@EDH+  (180-DHG)+ FGH=180                  5.substitution post from statements
                                               #2,4

6.@EDH+@FGH=@DHG                             6.addition and subtraction post.
                                               subtracted 180. added @DHG

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