# 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. 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 °.