Question

If E and F are the mid points of the non-parallel sides AD and BC of a trapezium ABCD resp.Show that EF =1/2(AB +DC) if given EF ∥ AB. BEST ANSWER WILL BE MARKED AS BRAINLIEST. WRONG ANSWER WILL BE REPORTED.

Answer 1

Answer:

Given,

Abcd is a trapezium and ab || cd. E and f are the mid points of bc and ad.

To prove,

1/2(ab + cd)

Construction,

Join be and produce it to meet cd produced at g.

Proof,

In ∆ edg and ∆ eab

Angle abe = angle egd.          [Alternate interior angles.]

De = ae         [ since, e is the mid point of ad.]

Angle aeb = angle ged       [vertically opposite angles.]

Therefore, ∆ edg congruent to ∆ eab  

By asa rule.

Ab = gd              [cpct]

Eb = eg              [cpct]

In ∆ cgb

Since, e is the mid point of eg [ since, ec  = eg]

Also, f is the mid point of bc.  [ Given]

Therefore, ef || gc and ef = 1/2 gc

By mid point theorem.

But, gc = gd + dc

Gc = ab + cd

That is, ef = 1/2( ab + cd )

Answer 2

Answer:

ANSWER

AB∥DC & EF∥DC, therefore

AB∥EF∥DC

Join AC which intersects EF at G. In △ADC ,

EG∥DC [∵EF is the extension of EG]

ED

AE

=

GC

AG

→(1) [Lines drawn parallel to one side of triangle intersects the other two sides in distinct points. Then it is divided the other two sides in same ratio]

Similarly in △ABC , AB∥GF , Therefore

FC

BF

=

GC

AG

→(2)

From (1) & (2) ,

ED

AE

=

FC

BF

Step-by-step explanation:

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