Question

$\text{ABCD is a parallelogram. What kind of quadrilateral is it if :}\left(i\right)AC=BD\text{and AC is perpendicular to BD ?}\left(ii\right)\text{AC is perpendicular to BD but is not equal to it ?}\left(iii\right)AC=BD\text{but AC is not perpendicular to BD ?}$

Answer 1

$\left(i\right)$

$AC=BD\text{(Given)}\&AC\perp BD\text{(Given)}\text{i.e. Diagonals of quadrilateral are equal and they are}\perp r\text{to each other.}\therefore \text{ABCD is square}$

$\left(ii\right)$

$AC\perp BD\text{(Given)}\text{But AC}\&\text{BD are not equal}\therefore \text{ABCD is a Rhombus.}$

$\left(iii\right)$

$AC=BD\text{but AC}\&\text{BD are not}\perp r\text{to each other.}\therefore \text{ABCD is a Rectangle.}$