Construction Of Quadrilaterals

Before we go into the construction of quadrilaterals, it is important to understand what a quadrilateral is. A quadrilateral is a polygon with four vertices and four sides, each of which contains four angles. Its inner angles add up to 360 degrees. In general, a quadrilateral has sides of varying lengths and angles of varying degrees. Squares, rectangles, and other quadrilaterals, on the other hand, are unique in that some of their sides and angles are equal.

Construction of Quadrilaterals where the following conditions are met-

(i) four sides and one diagonal

(ii)three sides and including two angles

(iii) two sides and three angles

(i) When four Sides and One Diagonal are provided

Let us assume you are needed to construct a quadrilateral PQRS where the dimensions are:

PQ = 5 cm, QR = 3 cm, RS = 5 cm, PS = 4 cm, and Diagonal SQ = 6 cm

Starting with a rough idea of the length of the dimensions, we need to draw an estimated diagram with our free hands.

Beginning the construction of the quadrilateral, follow the steps given below:

Draw a 5-cm-long line segment and label the endpoints S and R.
Make an arc from the point R above the line segment with your compass set to a radius of 3 cm.
Set the compass to a radius of 6 cm and draw an arc from the preceding arc's point S.
Draw a Q at the spot where the two arcs cross. S and Q, as well as R and Q, should be joined.
Make an arc from point Q using a compass with a radius of 5 cm.
Set the compass to a radius of 4 cm and draw an arc from the preceding arc's point S.
Make a P at the spot where the two arcs cross.
Make a connection between the points P and Q, as well as P and S.

You will get the quadrilateral PQRS of the required measurements.

(ii) When three Sides and Including two Angles are provided

Let us assume you are needed to construct a quadrilateral PQRS where the dimensions are:

QR = 6 cm, RS = 5 cm, PS = 4 cm, ∠S = 100°, ∠R = 120°

Starting with a rough idea of the length of the dimensions, we need to draw an estimated diagram with our free hands.

Now starting with the construction, the steps are:

Step 1: Draw a 5-cm-long line segment and label the endpoints S and R.

Step 2: Draw a line segment SR from the point R that is 120 degrees and another line segment SR from the point S that is 100 degrees using a protractor.

Step 3: Make an arc from the point S on the 100-degree line with your compass set to a radius of 4 cm. P represents the intersection of the arc with the line.

Step 4: Make an arc from point R on the 120-degree line using the compass with a radius of 6 cm. Mark the intersection of the arc and the line as Q.

Step 5: Connect the P and Q points.

You will get the quadrilateral PQRS of the required measurements.

(iii) When two Sides and Three Angles are provided

Let us assume you are needed to construct a quadrilateral PQRS where the dimensions are:

AB = 5 cm, BC = 3 cm, ∠A = 120°, ∠B = 110°, ∠C = 90°

The steps for the construction of the quadrilateral ABCD are:

Step 1: Draw a 5-cm-long line segment and label the endpoints A and B.

Step 2: Using a protractor, draw a line from point A to point B, establishing a 120-degree angle with the line segment AB.

Step 3: Using the protractor, draw a line from point B to point B, establishing a 110-degree angle with the line segment BA.

Step 4: Make an arc from point B on the 110-degree line with your compass set to a radius of 3 cm. The place where the arc intersects the line is labeled C.

Step 5: Draw a line from point C to line segment CB, producing a 90-degree angle using the protractor. The point where the arc intersects the 120-degree line is labeled D.

The quadrilateral ABCD of the relevant measures is obtained. Because a quadrilateral's internal angles add up to 360 degrees, you can check the measure of D, which should be 40 degrees (360 – [120 + 110 + 90]).