Question

ABCD is a trapezium in which AB||CD, E and
F are 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 in which AB∣∣DC and E,F are mid point of AD,BC  respectively

join CE and produce it to meet BA produced at G

In △EDC and △EAG

ED=EA (e is mid point of AD

=>∠CED=∠GEC (vertically opposite angles)

=>∠ECD=∠EGA (alternating angles)

since,

△EDC≅△EAG

=>CD=GA and EC=EG

in △CGB

E is a mid point CG  (EC=EG) proved

F is a mid point of BC (given)

since,

by mid point theorem EF∣∣AB and EF=21 but GB=GA+AB=CD+AB

 Hence,EF∣∣AB and EF=21(AB+CD)

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