QuadrilateralsClass 8 Mathematics Important Points

The sum of the measures of the four interior angles of any quadrilateral is always $360^\circ$. This property applies to all types of quadrilaterals, including convex and concave ones.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A fundamental property is that the opposite sides of a parallelogram are also equal in length.

In a parallelogram, opposite angles are equal. Adjacent angles, which are angles on the same side, are supplementary, meaning their sum is $180^\circ$.

The diagonals of a parallelogram bisect each other. This means they intersect at their midpoint. The diagonals are not necessarily equal in length.

A rectangle is a parallelogram with all four angles equal to $90^\circ$. Its opposite sides are equal and parallel.

The diagonals of a rectangle are equal in length and bisect each other. A quadrilateral whose diagonals are equal and bisect each other is always a rectangle.

A rhombus is a parallelogram with all four sides of equal length. Its opposite angles are equal, and adjacent angles are supplementary.

The diagonals of a rhombus bisect each other at right angles ($90^\circ$). The diagonals also bisect the angles of the rhombus.

A square is a quadrilateral with all four sides equal and all four angles equal to $90^\circ$. A square is a special type of rectangle, rhombus, and parallelogram.

The diagonals of a square are equal in length, bisect each other at right angles ($90^\circ$), and bisect the vertex angles into two $45^\circ$ angles.

A trapezium (or trapezoid) is a quadrilateral with at least one pair of parallel opposite sides. The sum of adjacent angles between the parallel sides is always $180^\circ$.

An isosceles trapezium is a trapezium where the non-parallel sides are equal. In an isosceles trapezium, the base angles are equal, and the diagonals are also equal in length.

A kite is a quadrilateral with two distinct pairs of equal-length adjacent sides. One of its diagonals is the perpendicular bisector of the other, and one pair of opposite angles are equal.

A quadrilateral is a parallelogram if any one of the following is true: both pairs of opposite sides are equal, both pairs of opposite angles are equal, or the diagonals bisect each other.

Squares are special rectangles and rhombuses. Rectangles and rhombuses are special parallelograms. Parallelograms are special trapeziums (if defined with at least one pair of parallel sides).