RBSE Solutions Class 9 Maths Chapter 9 Quadrilaterals Exercise 9.5

Question 1. Construct a trapezium ABCD in which AB || CD, AB = 4 cm, BC = 2.3 cm, CD = 2.8 cm and AD = 1.9 cm.
Answer:
Steps of construction:
1. Draw a line segment AB of 4 cm.
2. On line segment AB, mark a point E such that the length BE is the difference between AB and CD, which is \( 4 - 2.8 = 1.2 \) cm.
3. With point B as the center, draw an arc with a radius of 2.3 cm.
4. With point E as the center, draw another arc with a radius of 1.9 cm. This arc should cross the arc drawn from B at point C.
5. With point C as the center, draw an arc with a radius of 2.8 cm. This arc will intersect the line segment extending from A.
6. Connect points A to D, C to D, and B to C. The resulting figure ABCD is the required trapezium.
In simple words: First, draw the base line. Then use the given side lengths to create a guiding triangle and arcs to find the other corners of the trapezium, making sure the top and bottom lines are parallel.

🎯 Exam Tip: When constructing a trapezium, often a triangle is formed by drawing a line parallel to one of the non-parallel sides. This helps to determine the position of the vertices accurately.

Question 2. Construct a trapezium PQRS in which PQ || SR, PQ = 6 cm, RS = 3 cm, PS = 3 cm and QR = 5 cm.
Answer:
Steps of construction:
1. Draw a line segment PQ that is 6 cm long.
2. Using point P as the center, draw an arc with a radius of 3 cm. Mark point E on line segment PQ such that PE is 3 cm. (This point E is typically used to create a triangle by subtracting the length of the shorter parallel side from the longer one, i.e., \( \text{QE} = \text{PQ} - \text{SR} = 6 - 3 = 3 \) cm or \( \text{PE} = \text{PQ} - \text{SR} \) depending on the construction method.)
In simple words: Start by drawing the longest parallel side. Then, from one end of this line, measure a specific distance and mark a point that helps in forming the rest of the shape.

🎯 Exam Tip: Always check if all necessary information for the construction is given. If any steps are unclear or missing, identify what else is needed to complete the figure.

Question 3. Construct a trapezium ABCD in which AB || CD, AB = 8 cm, BC = 6 cm, CD = 4 cm and ∠B = 75°.
Answer:
Steps of construction:
1. Draw a line segment AB of 8 cm.
2. At point B, draw an angle of 75° using a protractor.
3. With point B as the center, draw an arc of 6 cm along the 75° line. This marks point C.
4. On line segment AB, mark a point E such that BE is the difference between AB and CD, which is \( 8 - 4 = 4 \) cm.
5. Connect points C and E to form line segment CE.
6. With point C as the center, draw an arc of 4 cm. Simultaneously, with point A as the center, draw another arc with a radius equal to the length of CE (this will also be the length of AD). These two arcs will intersect at point D.
7. Connect points A to D and C to D. The figure ABCD is the required trapezium.
In simple words: First, draw the base and an angle at one end. Then, use arcs to mark the other points for the sides. Finally, draw the remaining lines to complete the trapezium.

🎯 Exam Tip: Pay close attention to the angle measurements. Using a protractor accurately is crucial for correctly placing the vertices of the trapezium.

Question 4. Construct a trapezium ABCD in which AB || CD, AB = 4 cm, AD = 5 cm and ∠B = 90°.
Answer:
Steps of construction:
1. Draw a line segment AB of 4 cm.
2. At point B, draw a perpendicular line to AB to form an angle of 90°. With B as the center, draw an arc of 4 cm which intersects this perpendicular line at point C.
3. At point C, draw another perpendicular line (an angle of 90° to BC). From C, measure and mark a point E such that CE is a specific length (typically corresponding to the difference between parallel sides, or derived from other dimensions). In this case, assuming CD is parallel to AB and the figure is a right-angled trapezium.
4. With point A as the center, draw an arc of 5 cm. This arc will intersect the line extended from CE at point D.
5. Connect points D to A and D to C. The figure ABCD is the required trapezium.
In simple words: Start with the base and draw a right angle at one end. Use the given side lengths to find the other points by drawing arcs and lines. This creates a trapezium with a 90-degree corner.

🎯 Exam Tip: For right-angled trapeziums, ensure the 90° angles are drawn precisely. This forms a clear rectangular section within the trapezium, simplifying the construction.