Question

In a parallelogram ABCD, E and F are mid-points of AB and CD respectively show that the line segment AF and EC trisect the diagonal BD​

Answer 1

Answer:

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Answer 2

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GIVEN:-E and F are the mid point of sides AB and CD of the parallelogram ABCD whose diagonal is BD.

TO PROVE:-BQ=QP=PD

PROOF:-ABCD is parellogram(given)

ABIIDC and ABIIDC(opposite side is llgm)

E is the mid point of AB

AE=1/2AB.

.....((1))

F is the mid point CD

CF=1/2CD

CF=1/2AB -(2)

From 1 and 2

AE =CF.

Also AE || CF

Thus, a pair of opposite sides os a quadrilateral AECF are parallel and equal .

Quadrilateral,AECF id a parellogram

=EC || AF

=EQ || AP and QC II MF

In triangle BMA ,E. is the mid point of BA. given

EQ || AP. proved

BQ=LP

Similar by taking triangle CLD ,we can prove that DP=QP

From 3 and 4 we get

BQ=QP=PD

Hence, AF and CE trisect the diagonal AC.

$\textbf{Hope\: it\: helps\: you\: ❤️ }$