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Kinds of Quadrilaterals - Elements of a Parallelogram

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There are four sides and four angles in a parallelogram. Some of these are equal. There are some terms associated with these elements that you need to remember. 
Given a parallelogram ABCD in following fig.

`bar (AB)` and `bar (DC)`, are opposite sides. `bar (AD)` and `bar (BC)` form another pair of opposite sides.
∠A and ∠C are a pair of opposite angles; another pair of opposite angles would be ∠B and ∠D.
`bar (AB)` and `bar (BC)` are adjacent sides. This means, one of the sides starts where the other ends. 
∠A and ∠B are adjacent angles. They are at the ends of the same side. ∠B and ∠C are also adjacent.  

Property: The opposite sides of a parallelogram are of equal length.
Given : A parallelogram ABCD , AB || CD and AD || BC 

Prove : AB = CD and AD = BC 
Draw any one diagonal AC. 
Proof : In ∆ ABC and  ∆ CDA , we have :
∠1 = ∠2   ...  [Alternate angles, AB ||CD and CA is transversal ] 
∠3 = ∠4   ...  [Alternate angles AD || BC and AC is transversal ]
∆ ABC ≅ ∆ CDA   ...[ASA  Axioms]
AB = CD and AD = BC  [C.P.C.T]

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