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Polygon And Quadrilateral’s Properties
1. Polygon: – It is a closed plane figure bounded by three or more than three straight lines.
There are of two types of polygons.
Convex: A polygon in which none of its interior angle is more than 180°
Concave: A polygon in which at least one interior angle is more than 180°.
Regular Polygon: All the sides are equal and also all the interior angles are equal
Sum of Interior angles of a polygon = (n – 2) × 180
n → number of sides
2. Rectangle: –
- In a parallelogram with two adjacent angles A and B equal to each other, then the parallelogram is a rectangle or a square.
- Diagonals are equal and bisect each other, but not necessarily at right angles.
- For the given perimeter of rectangle, a square has maximum area.
- The figure farmed by joining the mid-points of the adjacent sides of rectangle is a rhombus.
- The quadrilateral formed by joining the mid points of intersections of the angle bisectors of a parallelogram is a rectangle.
3. Rhombus: –
- A parallelogram in which all sides are equal is called a rhombus.
- Diagonal of rhombus bisect each other at right angles, but they are not necessarily equal.
- Diagonal bisect the vertex angles.
- Sum of any two adjacent angles is 180°
- Figure formed by joining the mid-points of the adjacent sides of a rhombus is a rectangle
4. Parallelogram: –
- Opposite sides are parallel and equal.
- Opposite angles are equal.
- Sum of any two adjacent angles is 180°.
- Each diagonal divides a parallelogram into two congruent triangles.
- The parallelogram that inscribed in a circle is a rectangle.
- The parallelogram that circumcircle a circle is a rhombus
- A quadrilateral whose only one pair of sides is parallel and other two sides are not parallel.