Question

ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Show that EF divides non parallel sides in same ratio.

Answer 1

Step-by-step explanation:

Given:

• ABCD is a trapezium.
• AB is parallel to DC.
• E and F are mid points on AD and BC respectively.
• EF is parallel to AB

To Show:

• EF divides non parallel sides in same ratio i.e AE/ED = BF/FC

Construction:

• Join A to C such that AC intersect EF at X.

Solution: Here, EF || AB (given) and AB || DC. Therefore,

➛ EF || DC ( Lines parallel to the same line are parallel to each other )

Now, in ∆ADC,

$\implies{\rm }$ AE/ED = AX/XC....(1) [By BPT]

In ∆ABC,

$\implies{\rm }$ AX/XC = BF/FC....(2) [By BPT]

From equation (1) and (2) we got

• AE/ED = BF/FC

Hence, Proved.

Answer 2

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Hope this will help u