Trapezium. Types of Trapezium

author: Martin Marinov
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Българска версия:

D: Quadrangle with only two parallel sides is called trapezium

    D_____M_a__C
    /|         (|          |\
   / |          |          |  \
  /  | h       | h       | h\
 /_(|_____|_____|) _\
A   D₁       P a      C₁   B


Trapezium ABCD (AB || CD)
AB, CD - bases of the trapezium
AB>CD => AB = a - big base
                 CD = b - small base
AD = c and BC = d - legs
P = a + b + c + d - perimeter of a trapezium
A + D = B + C = 180°

D: The line segment joining the two bases and simultaneously perpendicular to them is called height of the trapezium

DD₁ = MP = CC₁ = h - height of the trapezium
S = (a+b).h:2 - area of the trapezium

О: Trapezium with one leg perpendicular to the bases is called right-angled trapezium
 
D____b____C
 |             |\
 |             |  \
 | h           | h \
 |.)_______|.) _\
A       b     C₁a-b B

Trapezium ABCD (AB||CD, ADAB)
AD=CC₁=h; if AB=a, CD=b, then AC₁=b and C₁B=a-b

D: Trapezium that have congruent legs is called isosceles trapezoid.

T: A trapezoid is isosceles if and only if its angles on one of the bases are congruent

T: A trapezoid is isosceles if and only if its diagonals are congruent