Geometry

The contrapositive of the following conditional statement: If a figure has four sides, then it is not a triangle.

A.If a figure does not have four sides, then it is a triangle.
B.If a figure is a triangle, then it does not have four sides.
C.If a figure is not a triangle, then the figure has four sides.
D.If a figure does not have four sides then it is not a triangle.
E.None of the above.

My answer: A

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  1. I have to write this on my brain first:

    hypothesis: If a cow, then a mammal
    converse: If a mammal, then a cow (maybe)
    inverse:If not a cow then not a mammal(maybe)
    contrapositive: if not a mammal, then not a cow - TRUE
    ok, now
    Hypothesis: if 4 sides, then not a triangle
    converse: if not a triangle, then not four sides (maybe)
    inverse: If not four sides, then a triangle(maybe)
    Contrapositive: If a triangle, then not 4 sides (TRUE)
    so I think B

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  2. converse:
    if not a triangle, then four sides (maybe)

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