Question

If M and N are the mid points of sides AB and DC of parallelogram ABCD,then prove that AMCN is a parallelogram.​

Answer 1

Answer:

AC = 4 AL  In a parallelogram ABCD, M and N are midpoints of AB and AD respectively. MN cuts the diagonal AC at L .

Step-by-step explanation:

Lets join BD which intersects AC at P

Now Δ AMN & ΔABD

M & N are mid points of AB & AD respectively

=> MN ║ BD

=> ML ║ BP

=> ΔAML ≈ ΔABP

=> AM/AB = AL / AP

=> 1/2  = AL/AP

=> AP = 2AL

Diagonals of parallelogram bisect each other

=> AP = AC/2

=> AC = 2AP

=> AC = 2(2AL)

=> AC = 4 AL

QED

Proved.

Answer 2

Step-by-step explanation:

• join BD which intersect AC at P
• Now prove that AMN similar to ABD
• so, AML similar to ABP
• then , El equal to AP that is equal to half AP
• Now prove that ABD congruent BCD,
• by CPCTC CP equal to AP
• that is AP equal to half AC
• now since AL equal to half AP then
• so l equal to 1 by 4 AC or AC equal to 4AL
• HENCE, PROVED