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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