RBSE Solutions Class 8 Maths Chapter 7 Construction of Quadrilaterals Exercise 7.1

Question 1. Construct a quadrilateral ABCD in which AB = 4.0 cm., BC = 6.0 cm., CD = DA = 5.2 cm. and AC = 8.0 cm.
Answer:
First, we need to draw a simple rough sketch of the quadrilateral with all the given measurements. This helps in planning the construction steps.

Here are the steps to construct the quadrilateral ABCD:
1. Start by drawing a line segment AB with a length of 4.0 cm.
2. From point B, draw an arc with a radius of 6.0 cm. From point A, draw another arc with a radius of 8.0 cm. These two arcs will cross each other at a point, which we label as C. Connect points A to C and B to C. This completes the triangle ABC.
3. Next, from point A, draw an arc with a radius of 5.2 cm. From point C, draw another arc, also with a radius of 5.2 cm. These two arcs will intersect at a point, which we label as D. Connect points A to D and C to D.
This process forms the required quadrilateral ABCD.

In simple words: First, draw triangle ABC using sides AB, BC, and diagonal AC. Then, find point D by using the lengths DA and CD from points A and C. Finally, connect all points to form the quadrilateral.

🎯 Exam Tip: Always start with a rough sketch to visualize the quadrilateral and its given measurements. This helps in breaking down the construction into simpler steps, usually by forming a triangle first.

Question 2. Construct a quadrilateral JUMP in which JU = 3.5 cm., UM = 4.0 cm., MP = 5.0 cm., PJ = 4.5 cm. and PU = 6.5 cm.
Answer:
First, make a rough sketch showing all the given measurements for the quadrilateral JUMP. This helps to plan the construction.

Here are the steps for construction:
1. Begin by drawing a line segment JU with a length of 3.5 cm.
2. From point U, draw an arc with a radius of 6.5 cm (this is for diagonal PU). From point J, draw another arc with a radius of 4.5 cm (for side PJ). These two arcs will cross at a point, which is P. Connect points U to P and J to P. This forms the triangle JUP.
3. Next, using P as the center, draw an arc with a radius of 5.0 cm (for side PM). From point U, draw another arc with a radius of 4.0 cm (for side UM). These two arcs will intersect at a point, which we label as M.
4. Finally, connect points P to M and U to M. This completes the quadrilateral JUMP.

In simple words: First, create triangle JUP using the given side lengths and one diagonal. Then, use the remaining side lengths from P and U to find the last point M, completing the quadrilateral.

🎯 Exam Tip: When constructing a quadrilateral with five measurements, always try to form a triangle using three measurements first, usually involving a diagonal. Then use the remaining two measurements to find the fourth vertex.

Question 3. Construct a parallelogram MORE in which MO = 3.6 cm., OR = 4.2 cm., MR = 6.5 cm. Measure the remaining sides and write them in your notebook.
Answer:
First, draw a rough sketch of the parallelogram MORE with the given measurements. Remember that opposite sides of a parallelogram are equal.

Here are the steps to construct the parallelogram MORE:
1. Start by drawing a line segment MO with a length of 3.6 cm.
2. From point O, draw an arc with a radius of 4.2 cm (for side OR). From point M, draw another arc with a radius of 6.5 cm (for diagonal MR). These arcs will intersect at a point, which we label as R. Connect points M to R and O to R. This forms the triangle MOR.
3. Since MORE is a parallelogram, we know that ME = OR = 4.2 cm and ER = MO = 3.6 cm. So, from point M, draw an arc with a radius of 4.2 cm. From point R, draw another arc with a radius of 3.6 cm. These arcs will intersect at a point, which we label as E. Connect points M to E and E to R.
This completes the parallelogram MORE.
The remaining sides are: ME = 4.2 cm ER = 3.6 cm

In simple words: First, draw one side and a diagonal to form a triangle. Then, use the property that opposite sides of a parallelogram are equal to find the last point and complete the shape. The missing sides will have the same lengths as their opposite sides.

🎯 Exam Tip: For parallelograms, always remember that opposite sides are equal and parallel. This property is crucial for construction, allowing you to deduce missing side lengths if you know one pair of opposite sides.

Question 4. Construct a rhombus BEST in which BE = 4.5 cm. and ET = 6.0 cm. Then measure the diagonals BS.
Answer:
First, draw a rough sketch of the rhombus BEST with the given side and diagonal measurements. Remember that all sides of a rhombus are equal.

Here are the steps to construct the rhombus BEST:
1. First, draw a line segment BE with a length of 4.5 cm.
2. Since all sides of a rhombus are equal, BT also has a length of 4.5 cm. From point B, draw an arc with a radius of 4.5 cm. From point E, draw an arc with a radius of 6.0 cm (for diagonal ET). These two arcs will intersect each other at a point, which we label as T. Connect points B to T and E to T. This forms the triangle BET.
3. Now, to find point S, from point T, draw an arc with a radius of 4.5 cm (for side TS). From point E, draw another arc with a radius of 4.5 cm (for side ES). These arcs will intersect at a point, which we label as S. Connect points E to S and T to S.
This completes the rhombus BEST.
Now, measure the diagonal BS from the constructed figure.
Upon measuring, the length of diagonal BS is approximately 6.7 cm.
In simple words: First, draw one side and a diagonal to make a triangle. Since all sides of a rhombus are equal, use this fact to find the last point and finish the rhombus. Then, measure the length of the other diagonal.

🎯 Exam Tip: Remember that a rhombus has all four sides equal. When one side and one diagonal are given, always assume the given side length applies to all sides for construction. The diagonals of a rhombus bisect each other at right angles.

Question 5. Construct a quadrilateral PQRS in which PQ = 4.4 cm., QR = 4.0 cm., RS = 6.4 cm., SP = 2.8 cm. and QS = 6.6 cm. Measure the diagonal PR.
Answer:
First, create a rough sketch of the quadrilateral PQRS, marking all the given side and diagonal lengths. This helps in planning the construction steps efficiently.

Here are the steps to construct the quadrilateral PQRS:
1. Start by drawing a line segment PQ with a length of 4.4 cm.
2. From point P, draw an arc with a radius of 2.8 cm (for side SP). From point Q, draw another arc with a radius of 6.6 cm (for diagonal QS). These two arcs will intersect at a point, which we label as S. Connect points P to S and Q to S. This forms the triangle PQS.
3. Next, from point S, draw an arc with a radius of 6.4 cm (for side RS). From point Q, draw another arc with a radius of 4.0 cm (for side QR). These two arcs will intersect at a point, which we label as R. Connect points Q to R and S to R.
This completes the quadrilateral PQRS.

The length of diagonal PR is 6 cm.
In simple words: First, draw triangle PQS using two sides and one diagonal. Then, use the remaining two sides from points Q and S to find point R. Finally, connect all points and measure the diagonal PR.

🎯 Exam Tip: When constructing any quadrilateral with five given measurements, always aim to form two triangles by using one common diagonal. This makes the construction systematic and easier to follow.