Question

Construct a rhombus whose diagonals are $16$ cm and $12$ cm. What property of the diagonals is used?

Answer 1

$\Rightarrow$ Draw a line segment $AC=16cm$

$\Rightarrow$ Draw a perpendicular bisector of $AC$, which intersect $AC$ at point $O.$

$\Rightarrow$ Take $O$ as center with radius $6cm$ and draw an arc above and below on perpendicular, We get point $B$ and $D$

$\Rightarrow$ Join $AB,BC,CD$ and $AD$

$\therefore$ $ABCD$ is required rhombus.

The properties which we have used are :

$\Rightarrow$ The intersection of the diagonals of a rhombus form $90$ degree angles. This means that they are perpendicular.

$\Rightarrow$ The diagonals of a rhombus bisect each other. This means that they cut each other in half.