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Types of Quadrilaterals - Properties of a Parallelogram

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definition

Parallelogram: A parallelogram is a quadrilateral whose opposite sides are parallel.

notes

Parallelogram:

A parallelogram is a quadrilateral whose opposite sides are parallel.

Properties of a Parallelogram:

  • A parallelogram has 4 sides.

  • The opposite sides of a parallelogram are equal in length.

  • The opposite angles of a parallelogram are equal.

  • A parallelogram has two diagonals. The diagonals of a parallelogram bisect each other.

  • Adjacent angles are supplementary (Sum of adjacent angles are 180°).
  • If a pair of opposite sides of a quadrilateral are equal and parallel, it is a parallelogram.

Element of a Parallelogram:

There are four sides and four angles in a parallelogram.

Given a parallelogram ABCD

  • Pair of opposite sides:
    i) `bar(AB) and bar(DC)`
    ii) `bar(AD) and bar(BC)`

  • Pair of opposite angles:
    i) ∠ A and ∠C
    ii) ∠ B and ∠ D.

  • Pair of adjacent sides:
    i) `bar(AB) and bar(BC)`
    ii) `bar(BC) and bar(CD)`
    iii) `bar(CD) and bar(AD)` 
    iv) `bar(AD) and bar(AB)` etc.

  • Pairs of adjacent angles:
    i) ∠A and ∠B
    ii) ∠ B and ∠C
    iii) ∠C and ∠D
    iv) ∠D and ∠A etc.

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