RBSE Solutions Class 8 Maths Chapter 7 Construction of Quadrilaterals Exercise 7.4

Question 1. Construct a quadrilateral KLMN, in which KL = 4.8 cm, LM = 5.0 cm, MN = 3.8 cm, ∠L = 72°, ∠M = 105°.
Answer: First, we draw a rough sketch to understand the measurements and plan our construction.

Steps for construction:

1. First, draw a line segment KL of length 4.8 cm.
2. At point L, draw a ray LX such that the angle ∠KLX is 72°. Then, from point L, cut an arc of 5.0 cm along LX and mark the point as M.
3. At point M, draw a ray MY such that the angle ∠LMY is 105°. From point M, cut an arc of 3.8 cm along MY and mark the point as N.
4. Finally, join point K to point N.

This way, KLMN is the required quadrilateral.

In simple words: To build this shape, first draw the bottom line. Then, from one end, make an angle and cut the length for the next side. Repeat this for the third side using the angle at the middle corner. Finally, connect the last two points to finish the shape.
🎯 Exam Tip: Always start with a rough sketch to visualize the quadrilateral and the order of construction steps. Use a sharp pencil and precise measurements for accurate results.

Question 2. Construct a quadrilateral ABCD, where AB = 3.0 cm, AD = 5.0 cm, BC = 3.0 cm, ∠A = 90°, ∠B = 105°.
Answer: First, we draw a rough sketch to plan the construction.

Steps for construction:

1. First, draw a line segment AB of length 3 cm.
2. At point A, construct an angle ∠BAX = 90° with AB. From point A, cut an arc of 5.0 cm along AX and mark the point as D.
3. Similarly, at point B, construct an angle ∠ABY = 105° with AB. From point B, cut an arc of 3 cm along BY and mark the point as C.
4. Finally, join point C to point D.

This completes the construction of quadrilateral ABCD.

In simple words: Start by drawing the base line AB. Then, from point A, draw a line upwards at a 90-degree angle and measure 5 cm for point D. From point B, draw another line at a 105-degree angle and measure 3 cm for point C. Finally, connect points D and C to complete the shape.
🎯 Exam Tip: When constructing quadrilaterals with two given angles and three sides, ensure the angles are drawn at the correct vertices and with the correct orientation relative to the given sides.

Question 3. Construct a quadrilateral PQRS where RS = 4.5 cm, RQ = 3.6 cm, SP = 5.0 cm, ∠R = 75°, ∠S = 120°.
Answer: First, we draw a rough sketch to guide our construction.

Steps for construction:

1. First, draw a line segment RS of length 4.5 cm.
2. At point R, construct an angle ∠SRX = 75° with SR. From point R, cut an arc of 3.6 cm along RX and mark this point as Q.
3. Similarly, at point S, construct an angle ∠RSY = 120° with RS. From point S, cut an arc of 5 cm along SY and mark this point as P.
4. Finally, join point P to point Q.

Thus, PQRS is the required quadrilateral.

In simple words: Draw the base line RS. At point R, make an angle of 75 degrees and mark 3.6 cm to find point Q. At point S, make an angle of 120 degrees and mark 5 cm to find point P. Then, connect Q and P to complete the shape.
🎯 Exam Tip: Always use a protractor to draw angles accurately and a ruler to mark exact lengths. A small error in angle or length can make the final figure incorrect.

Question 4. Construct a quadrilateral DEAR in which DE = 4.7 cm, EA = 5.0 cm, AR = 4.5 cm, ∠E = 60° and ∠A = 90°.
Answer: First, we draw a rough sketch to guide our construction.

Steps for construction:

1. First, draw a line segment DE of length 4.7 cm.
2. From point E, draw a ray EX making an angle of 60° with DE. From point E, cut an arc of 5.0 cm along EX and mark this point as A.
3. Similarly, at point A, draw a ray AY making an angle of 90°. From point A, cut an arc of 4.5 cm along AY and mark this point as R.
4. Finally, join point D to point R.

This completes the construction of quadrilateral DEAR.

In simple words: Draw the base line DE first. At point E, make a 60-degree angle and measure 5 cm for point A. At point A, make a 90-degree angle and measure 4.5 cm for point R. Finally, connect D and R to finish the quadrilateral.
🎯 Exam Tip: When angles are given at points that are not on the base line, you need to first construct the known side adjacent to that angle before drawing the angle itself.

Question 5. Construct a quadrilateral ABCD in which ∠B = 135°, ∠C = 90°, BC = 5.0 cm, AB = 9.0 cm and CD = 7.0 cm.
Answer: First, we draw a rough sketch to help us visualize the quadrilateral and plan the construction steps.

Steps for construction:

1. First, draw a line segment AB of length 9.0 cm.
2. At point B, construct an angle ∠ABX = 135°. From point B, cut an arc of 5.0 cm along BX and mark this point as C.
3. At point C, construct an angle ∠BCY = 90°. From point C, cut an arc of 7.0 cm along CY and mark this point as D.
4. Finally, join point A to point D.

This completes the construction of quadrilateral ABCD.

In simple words: Start with the longest side AB. At point B, draw an angle of 135 degrees and measure 5 cm to get point C. Then, at point C, draw a 90-degree angle and measure 7 cm to get point D. Finally, connect point A to point D to form the quadrilateral.
🎯 Exam Tip: When constructing quadrilaterals, always check if the given information (sides and angles) is sufficient and if it leads to a unique construction. Sometimes, more than one quadrilateral can be formed if not enough constraints are provided.