As shown in the figure, in ▱ ABCD, if the bisector AE of ∠ bad intersects BC at e, ad = 6, EC = 2, then the length of CD=______ ．

∵ AE bisects ∠ bad, ∵ BAE = ∵ DAE, and ∵ quadrilateral ABCD is parallelogram, ∵ DAE = ∵ AEB, ∵ BAE = ∵ AEB, ∵ Ba = be = bc-ec = 4, ∵ CD = AB = 4

As shown in the figure, in the trapezoidal ABCD, ad = BC, DC ‖ AB, m n e f are the bottom edge and the middle point of the diagonal respectively

Because ad = BC
DC‖AB
So the trapezoid ABCD is isosceles trapezoid
So diagonal DB = AC
In triangle ADB
AD‖ME ME=1/2AD
In the same way
BC‖MF=1/2BC
In triangle ADC
NF‖AD NF=1/2AD
In the same way
BF‖AD BF=1/2AD
So EM = en = NF = BF
And parallel to each other
So the quadrilateral menf is a diamond

RELATED INFORMATIONS

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