State whether the following statements are true or false. Justify your answers. A quadrilateral whose diagonals are equal Class 8

State whether the following statements are true or false. Justify your answers. A quadrilateral whose diagonals are equal Class 8

Question 1.

State whether the following statements are true or false. Justify your answers. Class 8

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

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

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

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

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

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

(vii) Isosceles trapeziums are parallelograms.

Solution:

(i) False; it will a rectangle.

(ii) True; because fourth angle will also be 90°.

(iii) True; it is a property of parallelogram.

(iv) False; diagonals must bisect each other for rhombus.

(v) True; it is a property of a parallelogram.

(vi) True, because each angle will be equal to 90°.

(vii) False, other pair of opposite sides must also be parallel.