RBSE Solutions Class 8 Maths Chapter 7 Construction of Quadrilaterals Exercise 7.3

Question 1. Construct a quadrilateral ABCD in which AB = BC = 3.0 cm, AD = CD = 5.0 cm and ∠ABC = 120°.
Answer:

In simple words: To draw this shape, first make the bottom line AB. Then, at point B, draw an angle of 120 degrees and mark point C on that line. Finally, use a compass to find point D by drawing arcs of 5 cm from both A and C, then connect D to A and C.
🎯 Exam Tip: Always start by drawing a rough sketch to visualize the quadrilateral. Use a sharp pencil and accurate compass settings for precise constructions.

Question 2. Construct a quadrilateral PQRS where PQ = 2.8 cm, PS = 3.3 cm, QR = 3.1 cm, SR = 2.6 cm and ∠P = 60°.
Answer:

In simple words: Start by drawing the base PQ. At point P, make an angle of 60 degrees and mark point S at a distance of 3.3 cm. Then, from S and Q, draw arcs with their respective lengths (2.6 cm and 3.1 cm) to find point R. Connect the points to complete the shape.
🎯 Exam Tip: When constructing quadrilaterals with specific side lengths and one angle, always build upon the known angle first. This helps to accurately position the other vertices.

Question 3. Construct a rectangle whose sides are 4.2 cm. and 2.5 cm. Measure its diagonal lengths.
Answer:

In simple words: First, draw the base line. Then, at both ends of the base, draw straight lines going up at 90 degrees. Mark the height on these lines. Connect the top two points to finish the rectangle. When you measure, both long lines going from corner to corner (diagonals) will be 4.9 cm. Rectangles always have equal diagonals.
🎯 Exam Tip: Remember that all angles in a rectangle are 90 degrees, and opposite sides are equal. The diagonals of a rectangle are also always equal in length.

Question 4. Construct a rhombus in which one angle is 75° and one side is 5.2 cm.
Answer:

In simple words: Start by drawing one side of 5.2 cm. At one end of this line, draw an angle of 75 degrees and mark the next point also 5.2 cm away. Then, use a compass to draw arcs of 5.2 cm from the two newly marked points. Where these arcs meet, that's the last corner. Connect all points to form the rhombus. A rhombus has all four sides equal in length.
🎯 Exam Tip: Remember that all four sides of a rhombus are equal. Once you've established two adjacent sides and an angle, the rest of the construction relies on simply drawing arcs of the same side length from the new points.

Question 5. Draw a square with one side of 5 cm.
Answer:

In simple words: To draw a square, first make one straight line (the base) that is 5 cm long. At one end of this line, draw a perfect 90-degree angle going upwards. Mark a point on this new line, also 5 cm away. Then, use your compass to draw arcs of 5 cm from the top two points. Where these arcs meet will be the last corner of your square. Connect all corners to finish the square. All four sides and all four angles (90 degrees) will be equal.
🎯 Exam Tip: For a square, remember that all sides are equal and all internal angles are 90 degrees. You can use two 90-degree constructions or a 90-degree and two arcs to complete it.