Revision Guide: Quadrilaterals

A quadrilateral is a polygon with four sides, derived from 'quadri' (four) and 'latus' (sides).

The sum of internal angles in any quadrilateral is 360°. This is crucial for angle-related problems.

Rectangles have four right angles and opposite sides equal. Squares have all sides equal and all angles 90°.

Rectangles have diagonals that are equal in length and bisect each other at midpoints.

Squares share all properties of rectangles plus diagonals that intersect at 90°, bisecting angles equally.

In rectangles, triangles formed by diagonals are congruent, establishing equal sides and angles.

A parallelogram is a quadrilateral with two pairs of parallel sides, which can lead to deeper geometric reasoning.

Opposite sides are equal, opposite angles are equal, and adjacent angles sum to 180°.

A rhombus has all sides equal, opposite angles equal, and diagonals that bisect each other at right angles.

A kite has two pairs of adjacent sides that are equal, with diagonals that intersect perpendicularly.

A trapezium is a quadrilateral with at least one pair of parallel sides. Isosceles trapeziums have equal non-parallel sides.

For any trapezium, the angles on the same side of a transversal sum to 180°.

While diagonals bisect each other in parallelograms, they are not necessarily equal.

In both squares and rhombuses, diagonals bisect each other at right angles, showcasing symmetry.

All angles in rectangles are 90°, which means no quadrilateral with non-equal opposite sides can be a rectangle.

Every square is a rectangle and a rhombus; however, not every rectangle or rhombus is a square.

Understanding how to construct shapes using properties of diagonals is essential in geometric constructions.

Remember the acronym 'PRISM' for properties: Parallel sides, Right angles in rectangles, Equal diagonals, Side equality in rhombuses.

While special quadrilaterals have distinct properties, general quadrilaterals lack consistent characteristics.

Understanding quadrilaterals helps in fields like architecture and engineering, where precise dimensions matter.