Question

Construct a rectangle $ABCD$. Diagonal $AC=8cm$ and angles between the diagonals$={45}^o$

Answer 1

$\Rightarrow$ Draw line segment $AC=8cm$

$\Rightarrow$ Draw a perpendicular bisector $PQ$ of the line segment $AC$ intersecting $AC$ at point $O$.

$\Rightarrow$ Draw a line $XY$ passing through point $O$ making an angle ${45}^o$ with $AC.$

$\Rightarrow$ Diagonals of a rectangle bisect each other.

$\Rightarrow$ Hence, take $O$ as the center and radius$=4cm$, cut two arcs on both sides of point $O$ cutting line $XY$ at points $B$ and $D$.

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

$\Rightarrow$ $ABCD$ is the required rectangle.