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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.

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B

Opposite angles are equal.

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C

Opposite angles are bisected by the diagonals.

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D

Diagonals bisect each other.

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Solution

## The correct options are B Opposite angles are equal. C Opposite angles are bisected by the diagonals. Since ABEF is a parallelogram, so AF∥BE and BF is the transversal. ∴∠AFB=∠FBE=x(alternate angles)..............(1) Also, since BCED is a parallelogram,BE || CD and BD is the transversal∴∠CDB=∠EDB=y(alternate angles) .............(2) Now, ∠FBD=∠FBE+∠EBD =x+y And, ∠AFE=∠BED(corresponding angles)∴∠AFE=z∠BED=∠BCD=z(opposite angles of a parallelogram)∠CDG+∠BCD=∠EBD+∠BED(sum of internal opposite angles equalts external angles of aΔ)⇒∠CDG=∠EBD+∠BED−∠BCD=y+z−y=z

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