Question

In the given figure, ACDF, ABEF and BCDE are all parallelograms. Using the information given in the figure choose the correct answer.

• 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

The correct option is C

Opposite angles are bisected by the diagonals.

(i) $AF||BE$ (given)

(ii) $\angle AFE=\angle BED=z$

(iii) $\angle FBE=\angle FBE=x$ (alternate angles)

(iv) $\angle EBD=\angle CDB=y$ (alternate angles)

(v) $\therefore \angle FBD=x+y$ (from (iii) and (iv))

(vi) $\angle BCD=\angle BED=z$ (Opposite angles of a parallelogram)

(vi) $\angle CDG=\angle BED=z$ (Corresponding angles)