Question

in the adjoining figure ABCD is parallelogram and E is the midpoint of AD. a line through D, drawn parallel to EB, meets AB produced at F & BC at L . prove that:
(i) AF =2DC
(ii) DF=2DL

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Answer 1

Step-by-step explanation:

ANSWER

Given, E is mid point of AD

Also EB∥DF

⇒ B is mid point of AF [mid--point theorem]

so, AF=2AB (1)

Since, ABCD is a parallelogram,

CD=AB

⇒AF=2CD

AD∥BC⇒LB∥AD

In ΔFDA

⇒LB∥AD

⇒

LD

LF

=

AB

FB

=1 from (1)

⇒LF=LD

so, DF=2DL

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Answer 2

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=> Refer to the attachment ✌️