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Question:


animallover
Student
High School - 10th Grade

How would you write a two column proof for the following statement?

Given: m<1= m<3+m<4

Prove: m<3+m<4+m<2=180

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Posted by animallover on Wednesday October 14, 2009 at 8:39 PM and tagged with geometry, math.

Answers:

  1. tandrewfield
    tandrewfield Teacher
    Middle School

    eNotes Editor

    Assuming this is about a 4-sided polygon whose angles will sum to 360, this is impossible to prove.  I will name the angles A,B,C, and D to make it easier to type.

    We know that A+B+C+D = 360. 

    If B+C+D = 180 (this is what you're trying to prove) then A, the remaining angle, is also 180 because 180+180=360.

    However, if A is 180, then C+D is also 180, based on the given.

    Substituting these values into A+B+(C+D) we get 180+B+180, which is a number greater than 360, and therefore not a quadrilateral.

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    Posted by tandrewfield on Wednesday October 14, 2009 at 9:33 PM

  2. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Is this a puzzle? There is no clarity in the question. From all the details we understand and interpret this as a question in geometry related with angles:

    I reconstruct the question as follows (sorry if I differ from your intention ):

    ABC is a triangle with angle A=m2 , angle B =m3 and angle C=m4. Produce AB upto D. Then Angle DBC is the exterior angle at B is m1.

    It is given that  m1=m3+m4.................(1)

    To prove m2+m3+m4=180 deg

    Add m2 to both sides of the equation at (1), then

    m1+m2=m3+m4+m2............................(2)

    But on the left side m1 and m2 are supplementary angle at B ,as DBC=m1 CBA=m2 and AD is the line AB extended .

    Therefore, m1+m2=180 deg and so,the value on the right side of the equation at (2) ,i.e, m2+m3+m4 is equal to 180 degree.

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    Posted by neela on Wednesday October 14, 2009 at 10:29 PM