trapeze is a flat geometric figure belonging to the group of quadrilaterals that has a pair of sides parallels:
The parallel sides of the trapezoids are called bases. The base that has the highest measurement is called larger base and the one with the smallest measure is called minor base.
Trapeze elements
Like the trapezoids they are polygons, they have the same elements common to all polygons, namely:
sides: are the straight segments that form the polygon;
vertices: are the meeting points between the sides;
internal angles: angles inside the polygon formed by two consecutive sides;
outside angles: angles on the outside of the polygon formed on one side and by the extension of the other, adjacent to the first;
diagonals: line segments that connect two non-consecutive vertices.
Properties common to all polygons
You trapezoids also have some properties that are common to all polygons.
a) A sum of internal angles of a trapeze is always equal to 360°. This is because the sum of the internal angles of any polygon is given by the expression: S = (n – 2)180.
b) An inside angle and the outside angle adjacent to it are always supplementary;
c) The perimeter on one trapeze is equal to the sum of the measurements of its four sides.
classification of trapezoids
isosceles trapezoids: are those that have congruent non-parallel sides;
Scalene trapezoids: are those that are not isosceles trapezoids;
rectangular trapezoids: are those in which one of the non-parallel sides forms a 90° angle with the base.
Trapeze Properties
1 - A line segment whose ends are the midpoints from the non-parallel sides of a trapeze is parallel to its bases and has a measure equal to arithmetic average the measurements of the bases;
2 – A area on one trapeze is given by the following expression:
A = (B + b) h
2
B = base major, b = base minor and h = height of trapezius.
3 – In one isosceles trapeze, the base angles are congruent;
4 – The diagonals of a isosceles trapeze are congruent.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-trapezio.htm
