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.

**A polygon in which none of its interior angle is more than 180°**

__Convex:__**A polygon in which at least one interior angle is more than 180°.**

__Concave:__**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

**5. Trapezium: –**

A quadrilateral whose only one pair of sides is parallel and other two sides are not parallel.

**Area of different geometric figures**