How do you construct a quadrilateral when its sides are given?

Answer 1

The lengths of the sides does not provide sufficient information to define a quadrilateral. This is because a quadrilateral can be flexed.

For example, given the facts that the lengths are all the same, the quadrilateral could be a square or a rhombus.

Answer 2

Remember a quadrilateral is a polygon that has 4 vertices and 4 sides enclosing 4 angles, the sum of its interior angles is 360 degrees. A quadrilateral (in general) has sides of different lengths and angles of different measures, however, squares, rectangles, are special types of quadrilaterals with some of their sides and angles being equal.

The following construction of quadrilaterals:

(1) 4 sides and 1 diagonal is given.

(2) 3 sides and including 2 angles are given

(3) 2 sides and three angles are given

Now starting with the construction, the steps are:

(Step 1) Draw a line segment of length 5 cm and mark the ends as S and R.

(Step 2) Construction of Quadrilaterals 2

(Step 3) Set your compass to the radius of 3 cm and make an arc from the point R above the line segment.

(Step 4) Set the compass to the radius of 6 cm and make an arc from the point S on the previous arc.

(Step 5) Mark the point as Q where the two arcs cross each other. Join the points S and Q as well as R and Q.

(Step 6) Construction of Quadrilaterals 3

(Step 7) Set the compass to the radius of 5 cm and make an arc from the point Q.

(Step 8) Set the compass to the radius of 4 cm and make an arc from the point S on the previous arc.

(Step 9) Construction of Quadrilaterals 4

(Step 10) Mark the point as P where the two arcs cross each other.

(Step 11) Join the points P and Q as well as P and S.

(Step 12) Construction of Quadrilaterals 5

Answer 3

By making four side with schale and pencil