Question

In the above figure, ACDF, ABEF and BCDE are all parallelograms. Analyse the given figure and chosse the correct option.

• A. Opposite sides are equal.
• B. Opposite angles are equal.
• C. Opposite angles are bisected by the diagonals.
• D. Diagonals bisect each other.

Answer 1

Answer: (B), (C)

The correct options are
B

Opposite angles are equal.

C

Opposite angles are bisected by the diagonals.

$\text{Since ABEF is a parallelogram, so}AF\parallel BE\text{and BF is the transversal.}$
$\therefore \angle AFB=\angle FBE=x\text{(alternate angles)..............(1)}$
$\text{Also, since BCED is a parallelogram,}\text{BE || CD and BD is the transversal}\therefore \angle CDB=\angle EDB=y\text{(alternate angles) .............(2)}$
$\text{Now,}$
$\angle FBD=\angle FBE+\angle EBD$
$=x+y$

$\text{And,}\angle AFE=\angle BED\text{(corresponding angles)}\therefore \angle AFE=z\angle BED=\angle BCD=z\text{(opposite angles of a parallelogram)}\angle CDG+\angle BCD=\angle EBD+\angle BED\text{(sum of internal opposite angles equalts external angles of a}\Delta )\Rightarrow \angle CDG=\angle EBD+\angle BED-\angle BCD=y+z-y=z$