Properties of Quadrilaterals Flashcards

Properties of Quadrilaterals

• Quadrilaterals are four-sided polygons, characterized by their interior angle sum of 360 degrees.

Types of Quadrilaterals

• Rectangle: A parallelogram where at least one angle measures 90 degrees.
• Square: A specific type of parallelogram that is both a rectangle (all angles 90 degrees) and a rhombus (all sides equal).
• Kite: A quadrilateral with two sets of adjacent sides that are congruent, forming a distinct shape.
• Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
• Trapezoid: A quadrilateral featuring exactly one pair of parallel sides, known as the bases.
• Isosceles Trapezoid: A trapezoid where the non-parallel sides are of equal length.
• Rhombus: A parallelogram with at least two consecutive sides that are equal in length.

Properties of Specific Quadrilateral Types

• Parallelogram Properties:

  • Opposite sides are equal in length.
  • Opposite angles are equal.
  • Diagonals bisect each other.
  • Consecutive angles are supplementary (add up to 180 degrees).

• Rhombus Properties:

  • Inherits all properties of parallelograms.
  • Diagonals intersect at right angles.
  • Diagonals bisect opposite angles.

• Rectangle Properties:

  • Inherits all properties of parallelograms.
  • Diagonals are equal in length.

• Square Properties:

  • Inherits all properties of parallelograms, rhombuses, and rectangles.

• Trapezoid Properties:

  • Two sets of consecutive angles are supplementary.

• Isosceles Trapezoid Properties:

  • Inherits all trapezoid properties.
  • Opposite angles are supplementary.
  • Base angles are equal.
  • Diagonals are equal.

• Kite Properties:

  • Diagonals intersect perpendicularly.
  • One pair of opposite angles are equal.
  • The long diagonal bisects the short diagonal and the opposite angles.

Relationships Among Quadrilaterals

• Quadrilaterals that have opposite sides parallel include parallelogram, rectangle, rhombus, and square.
• Quadrilaterals with only one pair of parallel sides are trapezoid and isosceles trapezoid.
• Those with opposite sides congruent are parallelogram, rectangle, rhombus, and square.
• Quadrilaterals where consecutive angles are supplementary include parallelogram, rectangle, rhombus, and square.
• A kite is uniquely defined by having two pairs of disjoint consecutive sides that are congruent.
• Opposite angles being congruent applies to parallelogram, rectangle, rhombus, and square.
• Only kites have exactly one pair of opposite angles that are congruent.
• Shapes with all angles right angles are rectangles and squares.
• Rhombuses and squares are defined by having all sides equal in length.
• Diagonal congruence applies to rectangles and squares only.
• Diagonals that bisect each other are a feature of parallelogram, rectangle, rhombus, and square.
• Perpendicular diagonals are characteristic of rhombus, square, and kite.
• A kite is defined by having diagonals that are perpendicular, with one diagonal bisecting the other.
• A square is the only quadrilateral where diagonals are congruent, perpendicular, and bisect each other.
• Rhombus and square diagonals bisect opposite angles, while kites feature one diagonal that bisects a pair of opposite angles.

True or False Statements

• A rhombus is a type of parallelogram (True).
• A square is classified as a trapezoid (False).
• A kite is indeed a quadrilateral (True).
• A parallelogram is always a rectangle (False).
• A square can be classified as a rectangle (True).
• An isosceles trapezoid is a form of trapezoid (True).
• A rectangle is a parallelogram (True).