Understanding Quadrilaterals

All the diagonals of a convex polygon lie entirely inside the polygon. In a concave polygon some diagonals will lie outside the polygon.

Each angle of a convex polygon is less than 180°.

At least one angle of a concave polygon is more than 180°.

All the sides and angles of a regular polygon are equal.

In an irregular polygon, all the sides and angles are not equal.

Sum of interior angles of a polygon with n sides = (n – 2) x 180° Each interior angle (regular polygon) = [(n – 2) × 180°] / n.

The sum of all the exterior angles of a convex polygon of n sides is always equal to 360°.

The sum of all the angles of a quadrilateral is 360°.

Opposite sides of a parallelogram are equal.

Opposite angles of a parallelogram are equal.

Diagonals of a parallelogram bisect each other.

Adjacent angles of a parallelogram are supplementary.

All sides of a rhombus are of equal length.

The diagonals of a rhombus are perpendicular bisectors of each other.

Opposite angles of a rhombus are of equal measure.

Opposite sides of a rhombus are parallel to each other.

The opposite sides of a rectangle are parallel to each other and are equal in length.

All angles of a rectangle are right angles.

The diagonals of a rectangle are equal in length and bisect each other.

A square is a rhombus in which each interior angle is equal to 90° and both the diagonals are equal.

A square is a rectangle in which all sides are equal and diagonals intersect at right angle.

The diagonals of a square are perpendicular bisectors of each other.

Keywords: Plane surface, Plane curve, Trapezium, Kite.

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