Math, asked by Macro, 6 months ago

ABCD is a trapezium, BC || AD, BC = 50 cm, AD = 80 cm. E and F are the mid-points of non-parallel sides of ABCD respectively. Prove that EF || BC and find the length of EF.​

Answers

Answered by hanshu1234
3

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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