6.5. Trapezoids and Kites http://www.ck12.org
T A=
√
(x−d)^2 +( 0 −y)^2 RP=√
(x−d− 0 )^2 +(y− 0 )^2=√
(x−d)^2 +(−y)^2 =√
(x−d)^2 +y^2=√
(x−d)^2 +y^2Notice that we end up with the same thing for both diagonals. This means that the diagonals are equal and we have
proved the theorem.
Midsegment of a Trapezoid
Midsegment (of a trapezoid):A line segment that connects the midpoints of the non-parallel sides.
There is only one midsegment in a trapezoid. It will be parallel to the bases because it is located halfway between
them. Similar to the midsegment in a triangle, where it is half the length of the side it is parallel to, the midsegment
of a trapezoid also has a link to the bases.
Investigation 6-5: Midsegment Property
Tools Needed: graph paper, pencil, ruler
- Draw a trapezoid on your graph paper with verticesA(− 1 , 5 ),B( 2 , 5 ),C( 6 , 1 )andD(− 3 , 1 ). Notice this is
NOT an isosceles trapezoid. - Find the midpoint of the non-parallel sides either by using slopes or the midpoint formula. Label themEand
F. Connect the midpoints to create the midsegment. - Find the lengths ofAB,EF, andCD. Can you write a formula to find the midsegment?
Midsegment Theorem:The length of the midsegment of a trapezoid is the average of the lengths of the bases, or
EF=AB+ 2 CD.
Example 4:Algebra ConnectionFindx. All figures are trapezoids with the midsegment.