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.
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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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