RBSE Solutions Class 8 Maths Chapter 7 Construction of Quadrilaterals Exercise 7.2

Question 1. Construct a quadrilateral LIFT when LI = 4.0 cm., IF = 3.0 cm., TL = 2.5 cm., LF = 4.5 cm. and IT = 4.0 cm.
Answer:

To construct the quadrilateral LIFT, we follow these steps:
1. First, draw a line segment LI that is 4.0 cm long.
2. From point L, draw an arc with a radius of 2.5 cm. From point I, draw another arc with a radius of 4 cm. These two arcs will cut each other at a point, which we label T. Connect points T to L and T to I. This forms triangle LIT.
3. Next, from point L, draw an arc with a radius of 4.5 cm. From point I, draw a third arc with a radius of 3.0 cm. These two arcs will intersect each other at a point, which we label F. Connect points L to F and I to F.
4. Finally, connect point T to F.
This process gives us the required quadrilateral LIFT.

In simple words: First, draw the base line LI. Then, use arcs to find point T and then point F, creating two triangles that join together. Finally, connect the last two points to complete the shape. Drawing a rough sketch first helps to plan the construction.

🎯 Exam Tip: Always start by drawing a rough sketch with all given measurements. This helps in visualizing the construction steps and ensures accuracy.

Question 3. Construct a quadrilateral PQRS. In which PS = 6.0 cm., SR = 5.0 cm., RQ = 7.5 cm., PR = 6.0 cm. and SQ = 10.0 cm.
Answer:

To construct the quadrilateral PQRS, follow these steps:
1. First, draw a line segment PQ that is 7.5 cm long.
2. From point P, draw an arc with a radius of 6 cm. From point Q, draw another arc with a radius of 10 cm. These two arcs will meet at a point, which we label S. Connect P to S and Q to S. This forms triangle PQS.
3. Next, from point P, draw an arc with a radius of 6 cm. From point Q, draw another arc with a radius of 7.5 cm. These arcs will intersect at a point, which we label R. Connect P to R, Q to R, and S to R.
This completes the construction of the required quadrilateral PQRS.

In simple words: Start by drawing one side and using two diagonals to find a third point. Then use other given sides to find the last point. This method uses diagonals to build the quadrilateral from triangles.

🎯 Exam Tip: When given diagonals, constructing triangles using the diagonals first can often simplify the overall construction process.

Question 4. Construct a quadrilateral ABCD in which AB = BC = CD = 5.0 cm. and Diagonals AC = 6.7 cm. and BD = 5.9 cm.
Answer:

To construct the quadrilateral ABCD, follow these steps:
1. First, draw a line segment AB that is 5 cm long.
2. From point A, draw an arc with a radius of 6.7 cm. From point B, draw another arc with a radius of 5.0 cm. These two arcs will meet at a point, which we label C. Connect A to C and B to C. This forms triangle ABC.
3. Next, from point B, draw an arc with a radius of 5.9 cm. From point C, draw another arc with a radius of 5 cm. These arcs will intersect each other at a point, which we label D.
4. Finally, connect B to D, C to D, and A to D.
This completes the construction of the required quadrilateral ABCD.

In simple words: Start by drawing the first side, then use the given side lengths and diagonal lengths to locate points C and D by drawing arcs. Once all points are found, connect them to make the quadrilateral. This construction shows how three equal sides can be part of a larger shape.

🎯 Exam Tip: When multiple sides are equal, it often simplifies certain construction steps. Always look for triangles formed by sides and diagonals to break down the construction.

Question 5. Construct a quadrilateral GOLD in which GO = 3.0 cm., OL = 2.5 cm., GD = 5.0 cm., GL = 4 cm. and OD = 7 cm.
Answer:

To construct the quadrilateral GOLD, follow these steps:
1. First, draw a line segment GO that is 3.0 cm long.
2. From point G, draw an arc with a radius of 4 cm. From point O, draw another arc with a radius of 2.5 cm. These two arcs will meet at a point, which we label L. Connect G to L and O to L. This forms triangle GOL.
3. Next, from point G, draw an arc with a radius of 5 cm. From point O, draw another arc with a radius of 7 cm. These arcs will intersect each other at a point, which we label D. Connect G to D and O to D. Also, connect D to L.
This completes the construction of the required quadrilateral GOLD.

In simple words: First, create a triangle (GOL) using three given lengths. Then, use the remaining lengths and one diagonal (OD) to find the fourth point (D). Finally, connect the last side to form the full quadrilateral. Thinking of quadrilaterals as two connected triangles helps in construction.

🎯 Exam Tip: For constructions involving many sides and diagonals, focus on building the quadrilateral in stages, usually by constructing one or two triangles first.