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]
Shaalaa.com | Elements of a parallelogram
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