There are different types of the quadrilateral on the basis of their nature of sides and their angle.
If a quadrilateral has one pair of parallel sides then it is a Trapezium.
Here AD∥BC in quadrilateral ABCD, hence it is a trapezium.
If the two pairs of adjacent sides are equal in a quadrilateral then it is called a Kite.
Here AB = BC and AD = CD
Properties of a kite
If the two pairs of opposite sides are parallel in a quadrilateral then it is called a Parallelogram.
Here, AB ∥ DC and BC ∥ AD, hence ABCD is a parallelogram.
Elements of a Parallelogram
Some terms related to a parallelogram ABCD
1. Opposite Sides – Pair of opposite sides are
AB and DC,
AD and BC
2. Opposite Angles – Pair of opposite angles are
∠ A and ∠C
∠B and ∠D
3. Adjacent Sides – Pair of adjacent sides are
AB and BC
BC and DC
DC and AD
AB and AD
4. Adjacent Angles – Pair of adjacent angles are
∠A and ∠B
∠B and ∠C
∠C and ∠D
∠A and ∠D
Properties of a Parallelogram
1. The opposite sides of a parallelogram will always be equal.
Here, AB = DC and AD = BC.
2. The opposite angles of a parallelogram will always be of equal measure.
∠A = ∠C and ∠D = ∠B.
3. The two diagonals of a parallelogram bisect each other.
Here in ABCD, AC and BD bisect each other at point E. So that AE = EC and DE= EB.
4. The pair of adjacent angles in a parallelogram will always be a supplementary angle.
If the opposite angles of a parallelogram are (3x + 5) ° and (61- x) °, then calculate all the four angles of the parallelogram.
As we know that the opposite angles are equal in a parallelogram so
(3x + 5)° = (61 – x) °
3x + x = 61- 5
4x = 56
x = 14°
By substituting the value of x in the given angles.
(3x + 5)° = 3(14) + 5
= 42 + 5 = 47°
(61 – x)° = 61 – 14
Both the angles are 47° as the opposite angles are equal.
Now to find the other angles let one of the adjacent angles to the above angle is z.
47° + z = 180° (adjacent angles are supplementary angles).
Z = 180° – 47°
The fourth angle will also be 133° as the opposite angles are equal.
Hence the four angles of the given parallelogram are 47°, 47°, 133° and 133°.