The proof that LMNO is a parallelogram from the given proof statements is that; LMNO has pair of parallel sides and hence, it is a parallelogram.
What is the proof of a quadrilateral?
From the given figure LMNO;
We are told that;
LM = NO and LO = MN.
If we consider the triangles LMN and LNO;
LM =ON (Given)
MN = OL (Given)
LN = LN (Reflexive property)
Now, with the aid of SSS congruency rule, ΔLMN ≅ ΔNOL
From CPCT Corresponding parts of congruent triangles are congruent, we can say that;
∠MLN = ∠ONL
These angles are alternate angles and hence, the sides LM and NO are parallel.
Thus, from the above two conclusions, it can be said that the quadrilateral LMNO has pair of parallel sides and hence, it is a parallelogram.
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