Question

The figure formed by joining the mid-points of the sides of a quadrilateral ABCD taken in order is a square only, if

• A. diagonals of ABCD are not equal.
• B. diagonals of ABCD are equal.
• C. diagonals of ABCD are equal and perpendicular.
• D. diagonals of ABCD are not perpendicular.

Answer 1

Answer: (C)

diagonals of ABCD are equal and perpendicular.

In $\Delta ABD$, EH ll BD (Mid-point theorem)

In $\Delta CBD$, FG ll BD (Mid-point theorem)

In $\Delta ACD$, GH ll AC (Mid-point theorem)

In $\Delta ABC$, EF ll AC (Mid-point theorem)

If AC is perpendicular to BD, then adjacent sides of quadrilateral EFGH are perpendicular => Rectangle/square

and If AC = BD, then adjacent sides are equal => Square