Quadrilaterals

A quadrilateral \( ABCD \) is a closed shape with four sides (edges) and four vertices. It is also called a polygon with four sides.
quadrilateral
The four interior angles of a quadrilateral add up to \( 360^{\circ} \), hence \( \quad \angle A + \angle B + \angle C + \angle D = 360^{\circ} \)
Special quadrilaterals such as parallelograms, trpaezoids, rectangles, squares, kites and rhombuses are presented with their properties.



Parallelogram

A parallelogram is a quadilateral with the opposite sides parallel.
parallelogram
Properties

  1. Opposite sides are congruent (equal length)
  2. The diagonals \( AC \) and \( BD \) bisects the at point \( O \) that divides each diagonal into equal parts: \( OA = OC \) and \( OB = OD \)
  3. The are several pairs of congruent triangles: \( \triangle ADB \) and \( \triangle CBD \) , \( \triangle ADC \) and \( \triangle ABC \) , \( \triangle ADO \) and \( \triangle BCO \) etc ...
  4. Opposite interior angles are congruent: \( \angle DAB = \angle DCB \) and \( \angle ADC = \angle ABC \)
  5. Several other angles are congruent: \( \angle ABO = \angle CDO \), \( \angle DAO = \angle BCO \), etc ...
  6. Area \( A_p \) of a parallelogram is given by: \( A_r = AB \times h\)
Parallelogram Problems and Calculator



Trapezoid

A trapezoid is a quadilateral with at least two opposite sides parallel.
trapezoid
Area \( A_t \) of a trapezoid is given by: \( A_t = \dfrac{1}{2} h \times (AB+DC) \)
Trapezoid Problems and Calculator



Rectangle


rectangle
Properties
A rectangle is a parallelogram with interior angles equal to \( 90^{\circ} \). Hence all properties of parallelograms are also property of rectangles and more properties are listed below.

  1. \( OA = OB = OC = OD \)
  2. \( \triangle ABC \), \( \triangle BCD \), etc ... are rigth triangles
  3. Area \( A_{re} \) of a rectangle is given by: \( A_{re} = AB \times BC\)
Rectangle Problems and Calculator



Square

A square is a rectangle with all sides equal.


square
Properties
All properties of rectangles are also property of squares and more properties are listed below.

  1. The diagonals intersect at angle of \( 90^{\circ} \)
  2. Area \( A_{s} \) of a rectangle is given by: \( A_{s} = AB^2\)
Problems on Squares and Calculator



Kite

A kite is a quadrilateral with two pairs of adjacent sides equal in length. In the diagram below, sides \( BA \) and \( BC \) have equal lengths and sides \( DA \) and \( DC \) have equal lengths.
kite
Properties

  1. The diagonals \( AC \) and \( BD \) bisects the at point \( O \) at an angle of \( 90^{\circ} \).
  2. The diagonals \( AC \) and \( BD \) bisects the at point \( O \) that divides the diagonal \( AC \) into equal parts: \( OA = OC \)
  3. \( BOA \), \( BOC\), \( DOA \) and \( DOC\) are right triangles.
  4. \( \angle ABO = \angle CBO \), \( \angle ADO = \angle CDO \), etc ...
  5. Triangles \( BOA \) and \( BOC \) are congruent, etc ...
  6. Area \( A_k \) of a kite is given by: \( A_k = \dfrac{1}{2} \times AC \times BD \)
Kite Questions with Solutions and Calculator



Rhombus

A rhombus is a parallelogram will all 4 sides equal in length.
rhombus
Properties

  1. The diagonals \( AC \) and \( BD \) bisects the at point \( O \) at an angle of \( 90^{\circ} \).
  2. The diagonals \( AC \) and \( BD \) bisects the at point \( O \) that divides the two diagonals into equal parts: \( OA = OC \) and \( OD = OB \)
  3. \( BOA \), \( BOC\), \( DOA \) and \( DOC\) are congruent triangles.
  4. \( \angle ABO = \angle CBO \), \( \angle ADO = \angle CDO \), etc ...
  5. Area \( A_{ro} \) of a parallelogram is given by: \( A_{ro} = \dfrac{1}{2} \times AC \times BD \)
Rhombus Problems and Calculator

More References and Links

Geometry Tutorials and Problems
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