Figure It Out: General Questions

Page 108: Question 11 (True/False)

(i) A quadrilateral whose diagonals are equal and bisect each other must be a square.

• False. It is a Rectangle. For a square, they must also be perpendicular.

(ii) A quadrilateral having three right angles must be a rectangle.

• True. Sum = $360$. Fourth angle = $360 - 270 = 90$. All angles 90 = Rectangle.

(iii) A quadrilateral whose diagonals bisect each other must be a parallelogram.

• True. This is a defining property.

(iv) A quadrilateral whose diagonals are perpendicular to each other must be a rhombus.

• False. This is true for a Kite as well. For a rhombus, they must also bisect each other.

(v) A quadrilateral in which opposite angles are equal must be a parallelogram.

• True.

(vi) A quadrilateral in which all angles are equal is a rectangle.

• True. $360/4 = 90^\circ$.

(vii) Isosceles trapeziums are parallelograms.

• False. Only one pair of sides is parallel.