Category : 8th Class
Understanding Quadrilaterals
Sample Figure |
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Numbers of sides, Vertices of the shape |
3,3,0. Triagle |
4,4,2 Quadrilateral |
5,5,5 Pentagon |
6,6,9 Hexagon |
7,7,14 Heptagon |
8,8,20 Octoagon |
e.g., A square (since all its sides are equal and all its angles are equal.)
\[\frac{{{360}^{o}}}{{{x}^{o}}}\]
e.g., A rectangle (though it is equiangular, it is not equilateral.)
Figure |
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Number of sides |
3 |
4 |
5 |
6 |
Angle sum |
\[{{180}^{o}}\] |
\[2\times {{180}^{o}}=\] \[\left( 4-2 \right)\times {{180}^{o}}\] |
\[3\times {{180}^{o}}\]\[\left( 5-2 \right)\times {{180}^{o}}\] |
\[4\times {{180}^{o}}=\]\[\left( 6-2 \right)\times {{180}^{o}}\] |
Thus, in general, the sum of interior angles of a polygon of 'n' sides is given by
\[\left( n-2 \right)\times {{180}^{o}}\text{ }or\text{ }\left( n-2 \right)\text{ }\times \text{ }2\]right angles or 2n - 4 right angles.
\[{{360}^{o}}\].
Types of quadrilaterals.
Definitions\[\to \] |
A quadrilateral with each pair of opposite sides parallel is called a parallelogram |
A Parallel - o gram having all sides equal is called a rhombus. |
A Parallel- Ogram is a rectangle if each of its angles is a right angle. |
A rectangle Having all its sides equal is called a square. |
A quadrilateral in which one pair of opposite sides is parallel is called a trapezium. |
A kite is quadrilateral formed by two isosceles triangles standing on the opposite sides of a common base. |
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S. No. |
Property |
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1. |
The diagonals bisect each other. |
Yes |
Yes |
yes |
Yes |
Not always |
yes |
2. |
Each diagonal bisects each pair of opposite angles . |
Not always |
Not always |
Not always |
Yes |
Not always |
Not always |
3. |
The diagonals divide the quatilateral into four |
Not always |
Not always |
Not always |
Yes |
Not always |
Not always |
4. |
The diagonals perpendicular to each other.
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Not always |
Yes |
Not always |
Yes |
Not always |
Yes |
5. |
The diagonals are equal. |
yes |
Not always |
Yes |
Yes |
Not always |
Not always |
6. |
Diagonals are equal and right bisectors of each other. |
Not always |
Not always |
Not always |
Yes |
Not always |
Not always |
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