Construct a quadrilateral given its diagonals two adjacent s

Construct a quadrilateral, given its diagonals, two adjacent sides, and the angle between the two remaining sides. Given three points A, B, and C, construct a line passing through A such that the distance between the perpendiculars to this line dropped from the points B and C is congruent to a given segment.

Solution

Let us suppose the quadrilateral is ABCD. and sides AB and AD is diven, diagonals AC and BD are given.

So first step is draw the base AB with given measure of the quadrilateral.

From, A draw an arc equal to the given measure. Also from B draw an arc with measure equal to BD intersecting the previous arc.

Name the intersecting point as D.

Now from B draw an angle with given degrees,

From A draw another arc with measure equal to AC intersecting the arm of angle drawn at B.

Finally Join BC, CD and BD.

Thus, we have the quadrilateral ABCD.