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Write a two-column proof. Given: Quadrilateral ABCD is a parallelogram; M is a midpoint of Segment AB; N is a midpoint of Segment DC Prove: Quadrilateral AMCN is a parallelogram

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Answer:

The answer is given below

Explanation:

Statement Reasons

ABCD is a parallelogram; M is a midpoint Given

of AB and N is a midpoint of Segment

AB//DC, therefore AM//NC For a parallelogram, opposite . sides are parallel to each other

AB≅DC For a parallelogram, opposite . sides are equal to each other

1/2AB≅1/2DC Since both sides are equal to . each other

1/2AB = AM and 1/2DC = NC M is the midpoint of AB and N . is the midpoint of DC Midpoint

. theorem

AM≅NC Substitution, since AB is also

. equal to BC

Quadrilateral AMCN is a parallelogram If opposite sides of a

. quadrilateral is equal and .

opposite, it is a parallelogram

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