Construction Of Quadrilaterals

Before talking about the construction of quadrilaterals, let us recall what a quadrilateral is. 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, etc. are special types of quadrilaterals with some of their sides and angles being equal. In this article, we will discuss the following construction of quadrilaterals:

Construction of Quadrilaterals where-

(i) 4 sides and 1 diagonal is given.

(ii) 3 sides and including 2 angles are given

(iii) 2 sides and three angles are given

(i) When 4 Sides and One Diagonal are Given

Let us say you are required to construct a quadrilateral PQRS where the measurements are:

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

For the construction of quadrilaterals with some of the measurements given, we first draw a rough figure of the quadrilateral with the given dimensions, as shown below.

Construction of Quadrilaterals 1

Now starting with the construction, the steps are:

  • Draw a line segment of length 5 cm and mark the ends as S and R.

Construction of Quadrilaterals 2

  • Set your compass to the radius of 3 cm and make an arc from the point R above the line segment.
  • Set the compass to the radius of 6 cm and make an arc from the point S on the previous arc.
  • Mark the point as Q where the two arcs cross each other. Join the points S and Q as well as R and Q.

Construction of Quadrilaterals 3

  • Set the compass to the radius of 5 cm and make an arc from the point Q.
  • Set the compass to the radius of 4 cm and make an arc from the point S on the previous arc.

Construction of Quadrilaterals 4

  • Mark the point as P where the two arcs cross each other.
  • Join the points P and Q as well as P and S.

Construction of Quadrilaterals 5

You obtain the quadrilateral PQRS of the required measurements.

(ii) When 3 Sides and Including 2 Angles are Given

Let us say you are required to construct a quadrilateral PQRS where the measurements are:

  • QR = 6 cm
  • RS = 5 cm
  • PS = 4 cm
  • ∠S = 100 degrees
  • ∠R = 120 degrees

For the construction of quadrilaterals with some of the measurements given, we first draw a rough figure of the quadrilateral with the given dimensions, as shown below.

Construction of Quadrilaterals 6

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.

Construction of Quadrilaterals 7

Step 2: Using a protractor, draw a line from point R making 120 degrees and another line from the point S making 100 degrees with the line segment SR.

Construction of Quadrilaterals 8

Step 3: Set your compass to the radius of 4 cm and make an arc from the point S on the 100-degree line. Mark the point as P where the arc intersects the line.

Step 4: Similarly, set the compass to the radius of 6 cm and make an arc from point R on the 120-degree line. Mark the point as Q where the arc intersects the line.

Construction of Quadrilaterals 9

Step 5: Join the points P and Q.

Construction of Quadrilaterals 10

You obtain the quadrilateral PQRS of the required measurements.

(iii) When 2 Sides and Three Angles are Given

Let us say you are required to construct a quadrilateral ABCD where the measurements are:

  • AB = 5 cm
  • BC = 3 cm
  • ∠A = 120 degrees
  • ∠B = 110 degrees
  • ∠C = 90 degrees

The steps for the construction of the quadrilateral ABCD are:

Step 1: Draw a line segment of length 5 cm and mark the ends as A and B.

Construction of quadrilaterals

Step 2: Using a protractor, draw a line from the point A making 120 degrees with the line segment AB.

Construction of Quadrilaterals Example

Step 3: Using the protractor, draw a line from point B making 110 degrees with the line segment BA.

Construction of Quadrilaterals 13

Step 4: Set your compass to the radius of 3 cm and make an arc from point B on the 110-degree line. Mark the point as C where the arc intersects the line.

Construction of Quadrilaterals 14

Step 5: Using the protractor, draw a line from point C making 90 degrees with the line segment CB. Mark the point as D where the arc intersects the 120-degree line.

Construction of Quadrilaterals 15

You obtain the quadrilateral ABCD of the required measurements. Since the sum of the interior angles of a quadrilateral is 360 degrees, you can check the measure of ∠D which should be equal to 40 degrees (360 – [120 + 110 + 90]).

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