#### notes

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]