Construct a parallelogram given diagonals and an angle show

Solution

Here we have given an angle and two diagonals. We will follow these steps to make parallelogram --

(1) First we make given angle with the help of compass.

(2) Then we draw the angle bisector by keeping compass once at low point of angle arc and once at high point of angle arc.

(3) Since adjacent angles of parallelogram are supplementary. So we calculate other angle and draw that also.

(4) Now we extend the line so that it cut the line (angle bisector).

(5) We repeat same process at other angle.

(6) At last, we join both intersection points.

Here our parallelogram is ready.