anonymous
  • anonymous
Can you prove DFG is congruent to MNP? Suppose DF is congruent to MN, DG congruent to MP, angle D is congruent to angle P. Can you prove that Triangle DFG is congruent to Triangle MNP? Explain your answer.
Mathematics
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1371147657532:dw|
anonymous
  • anonymous
Yes you can by since FD=NM then FG=NP and since it said DG= MP all the sides are congruent. IN additionally since Angle P=D than Angle M=G because it is an Isosceles. And then the top anle is the same because the other two angles are know and the angles in a triangle must add up to 180 degrees. Now that we know all the sides and angles and their all equal to each other than the triangles must be congruent.
jim_thompson5910
  • jim_thompson5910
IF the marked angle in triangle MNP was angle M (and not angle P), then you could use the SAS postulate

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jim_thompson5910
  • jim_thompson5910
but the angles are marked in two different spots, so I don't think it's going to work
jim_thompson5910
  • jim_thompson5910
I guess you could say that because the side opposite angle P is MN, and because MN = DF and you have 2 congruent sides, this must mean that angle G = angle P
jim_thompson5910
  • jim_thompson5910
so (not 100% sure), you can make this marking |dw:1371152407159:dw|
jim_thompson5910
  • jim_thompson5910
but that still doesn't help us with triangle MNP we still don't have the angle M (ie we can't show it's congruent to angle D) so it looks like you would have to use the SSA case...but that is not a valid congruence property
anonymous
  • anonymous
It must not be able to prove that DFG = MNP
jim_thompson5910
  • jim_thompson5910
yeah I don't think we can prove the two triangles are congruent
jim_thompson5910
  • jim_thompson5910
they may not be congruent (who knows)

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