RBSE Solutions Class 8 Maths Chapter 7 चतुर्भुज की रचना Exercise 7.2

Question 1. Construct quadrilateral LIFT where LI = 4.0 cm, IF = 3.0 cm, TL = 2.5 cm, LF = 4.5 cm, and IT = 4.0 cm.
Answer: We begin by drawing a rough sketch of the quadrilateral LIFT, marking all the given side lengths and diagonals.
Construction Steps:
1. 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 (for TL). From point I, draw another arc with a radius of 4.0 cm (for diagonal IT). The point where these two arcs intersect is T. Connect L to T and I to T.
3. Next, from point L, draw an arc with a radius of 4.5 cm (for diagonal LF). From point I, draw another arc with a radius of 3.0 cm (for side IF). The point where these arcs cross is F. Connect L to F and I to F.
4. Finally, connect point F to point T. This completes the quadrilateral LIFT, which is the shape we needed to draw. Understanding how diagonals divide a quadrilateral into triangles helps in planning the construction steps efficiently. In simple words: First, draw a rough picture of the quadrilateral and mark all the given lengths. Then, draw the first line. Use a compass to draw arcs from the ends of this line to find the other corners one by one. Connect all the points to finish the shape.

🎯 Exam Tip: Always draw a rough sketch first to visualize the quadrilateral and plan your construction steps accurately. This helps avoid mistakes and makes the process clear.

Question 2. Construct quadrilateral ABCD where AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm, and BD = 3.8 cm. Measure and write the length of side CD.
Answer: We start by drawing a rough sketch of the quadrilateral ABCD, marking all the given side lengths and diagonals.
Construction Steps:
1. Draw a line segment AB with a length of 3.8 cm.
2. From point A, draw an arc with a radius of 2.3 cm (for AD). From point B, draw another arc with a radius of 3.8 cm (for diagonal BD). The point where these arcs intersect is D. Connect A to D and B to D.
3. Next, from point A, draw an arc with a radius of 4.5 cm (for diagonal AC). From point B, draw another arc with a radius of 3.0 cm (for BC). The point where these arcs intersect is C. Connect A to C and B to C.
4. Finally, connect point C to point D. This forms the required quadrilateral ABCD. Upon measuring, the length of side CD is found to be 3.0 cm. Understanding how triangles are formed by diagonals within a quadrilateral simplifies the construction process. In simple words: First, draw AB. Then use a compass from A and B to find point D. After that, use the compass from A and B again to find point C. Join all points to make the quadrilateral. Finally, measure the length of CD.

🎯 Exam Tip: When constructing quadrilaterals, always use the diagonals to form triangles first. This helps to accurately locate the vertices. Ensure all given measurements are used.

Question 3. Construct quadrilateral PQRS where PS = 6.0 cm, SR = 5.0 cm, RQ = 7.5 cm, PR = 6.0 cm, and SQ = 10.0 cm.
Answer: We begin by drawing a rough diagram of the quadrilateral PQRS, noting down all the given side and diagonal measurements.
Construction Steps:
1. Draw a line segment SR measuring 5.0 cm.
2. From point S, draw an arc with a radius of 10.0 cm (for diagonal SQ). From point R, draw another arc with a radius of 7.5 cm (for side RQ). The point where these arcs meet is Q. Connect S to Q and R to Q.
3. Next, from point R, draw an arc with a radius of 6.0 cm (for diagonal PR). From point S, draw another arc with a radius of 6.0 cm (for side PS). The intersection point of these arcs is P. Connect S to P and R to P.
4. Finally, connect point P to point Q. This completes the construction of the quadrilateral PQRS. Using diagonals as a base for constructing triangles helps in precisely locating each vertex. In simple words: First, draw the line SR. Then, use compass arcs from S and R to find Q. After that, use compass arcs from R and S to find P. Connect all the points to form the quadrilateral.

🎯 Exam Tip: When five measurements are given, carefully identify which ones are sides and which are diagonals. This is key for picking the correct sequence of arcs to draw.

Question 4. Construct quadrilateral ABCD where AB = BC = CD = 5.0 cm, diagonal AC = 6.7 cm, and BD = 5.9 cm.
Answer: First, a rough sketch of quadrilateral ABCD is prepared, with all the given measurements for sides and diagonals marked.
Construction Steps:
1. Draw a line segment AB that is 5.0 cm long.
2. From point A, draw an arc with a radius of 6.7 cm (for diagonal AC). From point B, draw another arc with a radius of 5.0 cm (for side BC). The point where these two arcs intersect is C. Connect A to C and B to C.
3. Next, from point C, draw an arc with a radius of 5.0 cm (for side CD). From point B, draw another arc with a radius of 5.9 cm (for diagonal BD). The point where these arcs intersect is D. Connect D to B and D to C.
4. Finally, connect point A to point D. This completes the quadrilateral ABCD. Constructing quadrilaterals by first forming triangles using known side and diagonal lengths is a standard and reliable method.
In simple words: Draw line AB. Then use a compass from A and B to find point C. Next, use a compass from C and B to find point D. Connect A to D to finish the quadrilateral.

🎯 Exam Tip: When multiple sides are equal (like AB=BC=CD), pay extra attention to which points are being connected by which length to avoid confusion.

Question 5. Construct quadrilateral GOLD where GO = 3.0 cm, OL = 2.5 cm, GD = 5.0 cm, GL = 4.0 cm, and OD = 7.0 cm.
Answer: We start by drawing a rough diagram of the quadrilateral GOLD, marking all the given side and diagonal measurements.
Construction Steps:
1. Draw a line segment GO that is 3.0 cm long.
2. From point G, draw an arc with a radius of 4.0 cm (for diagonal GL). From point O, draw another arc with a radius of 2.5 cm (for side OL). The point where these arcs intersect is L. Connect G to L and O to L.
3. Next, from point G, draw an arc with a radius of 5.0 cm (for side GD). From point O, draw another arc with a radius of 7.0 cm (for diagonal OD). The point where these arcs intersect is D. Connect D to G and D to O.
4. Finally, connect point L to point D. This completes the construction of the quadrilateral GOLD. Using a compass and ruler accurately is crucial for precise geometric constructions. In simple words: Draw the line GO first. Then use arcs from G and O to find point L. After that, use arcs from G and O again to find point D. Connect L and D to finish the quadrilateral.

🎯 Exam Tip: Always check the spelling of the quadrilateral's vertices (e.g., GOLD) to ensure you connect the points in the correct order to form the desired shape.