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- Draw a line segment of length 5 cm and mark the ends as S and R.
- 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.
- 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.
- Mark the point as P where the two arcs cross each other.
- Join the points P and Q as well as P and S.
- 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.
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: 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.
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.
Step 5: Join the points P and Q.
You obtain the quadrilateral PQRS of the required measurements.
Close- Draw a line segment of length 5 cm and mark the ends as S and R.
- 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.
- 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.
- Mark the point as P where the two arcs cross each other.
- Join the points P and Q as well as P and S.
- 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.
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: 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.
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.
Step 5: Join the points P and Q.
You obtain the quadrilateral PQRS of the required measurements.
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