Given: overline LM cong overline ON and overline LO cong overline MN Prove : LMNO is a parallelogram

LMNO is a plane shape which has the properties of a parallelogram. It is has been proven to be a parallelogram.

A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.

To prove that LMNO as given in the question is a parallelogram:

i. The opposite sides of a parallelogram are congruent.

Thus,

/LM/ ≅ /ON/ (opposite side property)

/LO/ ≅ /MN/ (opposite side property)

ii. The opposite sides are parallel to each other.

i.e LM || ON

and

    LO || MN

ii. Consecutive angles are supplementary.

i.e <MLO + <LMN =

also

    <LON + <MNO =

iii. The diagonals are at right angles to each other.

LN ⊥ MO

iv. Opposite angles are congruent.

<LMN ≅ <LON

and

<MLO ≅ <MNO

Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.

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