Question

In trapezul ABCD cu bazele [AB] si [CD] , AC∩BD = {o} . Diagonalele [AC] si [BD] intersecteaza linia mijlocie [MN] ( M∈[AD] ) in punctele E si F .

a) Daca AB = 18 cm si CD = 6 cm , calculati MN si EF
b) Daca AB = 26 cm si MN = 18 cm , calculati CD si EF
c) Daca AB = 20 cm si EF = 6 cm , calculati CD si MN 
d) Daca MN = 22 cm si EF = 8 cm , calculati AB si CD

Answer 1

a)MN =18+6/2 =24/2 =12cm

EF =18-6/2 =12/2 =6 cm

b)26+CD /2 =18

CD =2*19-26 =36-26 =10 cm

EF =26-10/2 =15/2 =8 cm

c) 6 =26-CD/2

CD =26-12 =14 cm

MN=26+14/2

MN =40/2 =20 cm

d)AB+CD/2 =22

AB+CD =44

AB-CD /2 =8

AB-CD=2*8 =16

AB+CD =44  -

AB-CD=16

--------------------

/ 2CD =28

CD =14 cm

AB=44-14 =30 cm