What are adjacent sides and angles

Calculating on the square solutions

In this section you will find the solutions to the exercises and tasks for the article "Arithmetic on a square". First work on these tasks yourself and only then look at our solutions.


Solution to task 1: answer the questions

1a) A flat figure enclosed by four lines is called a square.

1b)

  • scope: The sum of all line lengths is called the circumference of the quadrilateral.
  • Angle sum: If you add the sum of all interior angles - see graphic above - you get 360 degrees, like a circle
    • Angle sum = 360 ° = α + β + γ + δ
  • information: A quadrilateral has four corners, four interior angles and four delimiting segments

1c) There are two different types of quadrilaterals: convex and concave. If all diagonals lie within the rectangle, it is called convex, otherwise it is called concave.

1d) Rectangle, square, parallelogram, trapezoid and diamond / rhombus

1e) rectangle:

  • A rectangle is enclosed by four lines
  • Opposite sides are the same length and parallel.
  • The two diagonals are the same length and bisect each other.
  • The sum of all angles is 360 degrees

1f) square:

  • the four sides are the same length
  • the four interior angles are the same size
  • it has four axes of symmetry
  • it is 4-fold rotationally symmetrical
  • it is point symmetric
  • the two diagonals are the same length

1g) parallelogram:

  • Two opposite sides are parallel and of the same length
  • The sum of neighboring angles is 180 °
  • The opposite angles are the same
  • The diagonals bisect each other
  • The center of symmetry is the intersection of the diagonals.

1h) trapezoid:

  • A square with at least two parallel sides
  • The two parallel sides are called the base of the trapezoid.
  • One of these base sides (usually the longer one) is often referred to as the base of the trapezoid, the two adjacent
    Sides as legs.
  • The height h of the trapezoid is the distance between the two parallel sides.
  • Each trapezoid has two diagonals that intersect in equal proportions.

1i) diamond:

  • A diamond is a flat convex square with four sides of equal length (equilateral square)
  • The opposite sides are parallel to each other
  • The two diagonals are axes of symmetry.
  • The diagonals are perpendicular to each other and bisect each other.
  • Opposite angles are the same size
  • The angle sum of all interior angles is 360 °.
  • Adjacent angles add up to 180 °.

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