Properties of Quadrilaterals and Parallelograms

A quadrilateral whose diagonals bisect each other and are perpendicular is a rhombus.

A quadrilateral having two opposite sides parallel and not congruent could be a trapezoid.

The quadrilateral that has diagonals that always bisect its angles and each other is a rhombus.

If the diagonals of a quadrilateral are congruent but do not bisect each other, it is an isosceles trapezoid.

Among a square, rectangle, and rhombus, the square and rhombus must have perpendicular diagonals.

To prove a parallelogram is a rhombus, you can show the diagonals are perpendicular.

If ABCD is a parallelogram, the statement $ ar{AC} ot ar{BD} $ proves it is a rhombus.

A parallelogram is always a rectangle if the diagonals are congruent.

Connecting the midpoints of the sides of a quadrilateral results in a parallelogram.

In rhombus ABCD, if $ AE = 5 $ and $ BE = 12 $, then $ ar{AB} = 13 $ using the Pythagorean theorem.

A rhombus has diagonals that bisect each other and are perpendicular, and all sides are equal.

A trapezoid has at least one pair of parallel sides, but the other sides are not necessarily equal.

A rectangle has opposite sides equal and all angles equal to 90 degrees.

A square is a special rectangle with all sides equal and all angles being right angles.

In a parallelogram, opposite angles are equal, which helps define its properties.

An isosceles trapezoid has congruent legs and bases that are parallel.

Congruent diagonals are found in rectangles and isosceles trapezoids, affecting their shape.

The diagonals of a quadrilateral can tell us important properties about the shape, like whether it's a rhombus or rectangle.

If all angles in a quadrilateral are equal, it's a rectangle or square.