Q10 of 56 Page 82

E is the mid-point of a median AD of DABC and BE is produced to meet AC at F. Show that AF = AC.


Given, a ABC in which AD is a median and E is mid-point of AD. Now, drawing DP||EF.


In ΔADP, E is mid-point of AD and EF||DP.


F is mid-point of AP.


In ΔFBC, D is mid-point of BC and DP||BF.


P is mid-point of FC.


Thus, AF = FP = PC


Hence, AF = AC


Hence, proved.


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E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD. Prove that EF || AB and EF = (AB + CD).

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