Central Median of Trapezium

author: Martin Marinov
viewed: 1655 times
Българска версия:

    D____b____C
   _/_              _\_
 M/_____m ___ \N
. /.                      .\.
 /______a ______\
A                            B

D: The line that connects the midpoints of the legs of a Trapezium is called central median of a trapezium:

Trapezium ABCD (AB||CD):
                              __
M - midpoint of AD      \_  MN - central median
N - midpoint of BC  __/

T: The central median of Trapezium is parallel to the bases and equals their sum divided by 2.

ABCD (AB||CD):

AM=MD, BN=CN

=> MN || AB || CD и MN = (AB + CD) (т.е. m = a+b )
                                               2                         2

Т: The line crosses one of the legs of a trapezium in the midpoint and is parallel to the base, then it crosses other leg in the midpoint.