PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoA four-sided closed two-dimensional shape is called a quadrilateral. It has four vertices, four sides and four angles.
Angle sum property of a quadrilateral
The sum of the angles of a quadrilateral is \(360º\).
Proof:
Given: \(ABCD\) is a quadrilateral.
Construction: Join \(BD\).
Now, we divided the quadrilateral into two triangles \(BAD\) and \(BCD\).
\(\angle B = \angle ABD + \angle DBC\) - - - - - (I)
\(\angle D = \angle ADB + \angle BDC\) - - - - - (II)
We know that "sum of all the angles of a triangle is \(180^\circ\)".
In \(\Delta BAD\):
\(\angle DAB + \angle ABD + \angle BDA = 180^\circ\) - - - - (III)
Similarly, in \(\Delta BCD\),
\(\angle DBC + \angle BCD + \angle CDB = 180^\circ\) - - - - (IV)
Adding equations (III) and (IV), we get:
\(\angle DAB + \angle ABD + \angle BDA + \angle DBC + \angle BCD + \angle CDB = 180^\circ + 180^\circ\)
Rearrange the angles.
\(\angle DAB + (\angle ABD + \angle DBC) + \angle BCD + (\angle BDA + \angle CDB) = 360^\circ\)
\(\angle A + \angle B + \angle C + \angle D = 360^\circ\) [using equations (I) and (II)]
That is, the sum of the angles of a quadrilateral is \(360^\circ\).
Types of quadrilateral
Name | Picture | Properties |
Parallelogram | 1. Opposite sides are equal and parallel. 2. Opposite angles are equal. 3. Diagonals bisect each other. | |
Square | 1. All sides are equal and parallel. 2. All interior angles are \(90^\circ\). 3. Diagonals bisect each other at right angles. | |
Rectangle | 1. Opposite sides are equal and parallel. 2. All interior angles are \(90^\circ\). 3. Diagonals bisect each other. | |
Rhombus | 1. All sides are equal. 2. Opposite angles are equal. 3. Diagonals are perpendicular. | |
Trapezium | 1. The bases of a trapezium are parallel. 2. Sum of adjacent angles on non-parallel sides are supplementary. | |
Kite | 1. Diagonals are perpendicular. 2. Diagonals bisect the vertex angles. 3. Non-vertex angles are congruent. 4. Two disjoint pairs of consecutive sides are congruent. |
Properties of a quadrilateral
1. A square, rectangle and rhombus are all parallelograms.
2. A square is a rectangle and also a rhombus.
3. A rectangle or a rhombus is not a square.
4. A parallelogram is a trapezium, but a trapezium is not a parallelogram.
5. A kite is not a parallelogram.