Are the diagonals of a rectangle perpendicular

 

Types of quadrilaterals

Special quadrilaterals can be derived from the general quadrilateral and defined in various ways.

Note that there are different ways of defining quadrilaterals. Depending on which properties you refer to (side lengths, diagonals, symmetry, interior angles, etc.), different definitions can be given.

     square

Some possible definitions:
  • A square with 4 sides of equal length and a right angle is called a square.
  • A rectangle with 3 right angles and two diagonals of equal length is called a square.
  • A rectangle with diagonals of equal length that bisect each other at right angles is called a square.

    rectangle

Some possible definitions:
  • A square with 3 right angles is called a rectangle.
  • A square with diagonals of equal length and bisecting each other is called a rectangle.
  • A square with a right angle, the opposite sides of which are each of the same length, is called a rectangle.

    parallelogram

Some possible definitions:
  • A square, the opposite sides of which are parallel to each other, is called a parallelogram.
  • A rectangle in which opposite angles are each equal is called a parallelogram.
  • A square, the diagonals of which are mutually halved, is called a parallelogram.

    Rhombus

Some possible definitions:
  • A square with 4 sides of equal length is called a diamond.
  • A square with diagonals bisecting at right angles is called a diamond.
  • A square with 2 sides parallel and the diagonals perpendicular to each other is called a diamond.

    Dragon

Some possible definitions:
  • A square that consists of 2 pairs of neighboring sides of equal length is called a kite.
  • A square in which the diagonals are perpendicular to each other and one diagonal is halved by the other is called a kite.
  • A square that is axially symmetrical with respect to a diagonal is called a kite.

    Leaning kite

Some possible definitions:
  • A square in which one diagonal is halved by the other is called a crooked kite.
  • An obliquely symmetrical square is called a crooked kite.

    Trapezoid

Some possible definitions:
  • A square with two opposite sides parallel to each other is called a trapezoid. Each of these sides is called the base or base side, the other two are called the legs.
  • A square in which 2 neighboring angles complement each other to 180 ° is called a trapezoid.
  • A square in which one side can be mapped onto another by centric stretching is called a trapezoid.

   

task

1. Test your knowledge with a few short exercises on types of squares (1) and (2).

   

2. Show that the sum of the opposite angles in the chordal quadrilateral is 180 °.