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Construction of Parallelogram When Two Adjacent Sides and One Diagonal Are Given.

State true or...

Question

State true or false:
The alongside figure shows a parallelogram $A B C D$ in which $A E = E F = F C$ , then
$D E = F B$

A

True

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B

False

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Solution

The correct option is A True
Between
$△ A D E a n d △ F B C A E = F C$ (given)
$∠ D A E = ∠ F C B$ ( because AD $∥$ BC)
$A D = B C S o, △ A D E ≅ △ F B C \Rightarrow D E = B F$

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