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grigory [225]
3 years ago
9

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

t DC Prove: Quadrilateral AMCN is a parallelogram
Mathematics
1 answer:
Zigmanuir [339]3 years ago
6 0

Answer:

The answer is given below

Step-by-step 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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