Question

ABCD is a trapezium in which AB||CD, E and Fare
the mid points of AD and BC respectively such
that EF || AB, If AB = 12 cm and EF = 10 cm then
CD​

Answer 1

Step-by-step explanation:

ABCD is a trapezium and E,F are mid-points of diagonal AC and BD

AB∥CD                [ one par of opposite side is parallel in trapezium ]

In △CDF and △GBF

⇒  DF=BF                   [ Since, F is mid-point of diagonal BD ]

⇒  ∠DCF=∠BGF   [ DC∥GB and CG is a transversal ]

⇒  ∠CDF=∠GBF    [ DC∥GB and BD is a transversal ]  

∴  △CDF≅△GBF       [ By ASA congruence rule ]

⇒  CD=GB         [ C.P.C.T ]     ---- ( 1 )

In △CAG, the points E and F are the mid-points of AC and CG respectively.

∴  EF=21(AG)

⇒  EF=21(AB−GB)

From ( 1 )

⇒  EF=21(AB−CD)