Rbse solutions for class 9 maths chapter 9 quadrilaterals ex 9.5

1. Class 9 Ex 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.
Solution.
Steps of construction:
1. Draw AB = 4 cm.
2. On AB mark a point E such that BE = AB – CD = 4 – 2.8 = 1.2 cm.
3. With centre B, draw an arc of 2.3 cm.
4. With centre E, draw an arc of 1.9 cm which intersects the previous arc at C.
5. With centre C, draw an arc of 2.8 cm which intersects the line segment which is coming
through A.
6. Join AD, CD and BC.
Hence, ABCD is required trapezium.
Question 2.
Construct a trapezium PQRS in which PQ || SR, PQ = 6 cm, RS = 3 cm, PS = 3 cm and QR =
5 cm.
Solution.
Steps of construction:
1. Draw a line segment PQ = 6 cm.
2. By taking P as centre take an arc of 3 cm and cut line segment PQ at E.
3. Now taking E as centre, draw an arc of 3 cm and also by taking Q as centre draw an arc of
5 cm which cuts the previous arc at R.
4. By taking R as centre, draw an arc of 3 cm and finally cut this arc by taking an arc of 3 cm
from P. This will be the required trapezium PQRS.

2. Question 3.
Construct a trapezium ABCD in which AB || CD, AB = 8 cm, BC = 6 cm, CD = 4 cm and ∠B
= 75°.
Solution.
Steps of construction:
1. Draw AB = 8 cm.
2. At B draw an angle of 75°.
3. With centre B draw an arc of 6 cm.
4. On AB, mark a point E such that BE = difference of AB and CD i.e. 8 – 4 = 4 cm.
5. Join CE.
6. With centre C, draw an arc of 4 cm and with centre A draw an arc of CE = AD. These arcs
intersect at point D.
7. Join AD and CD. Hence, ABCD is the required trapezium.
Question 4.
Construct a trapezium ABCD in which AB || CD, AB = 4 cm, AD = 5 cm and ∠B = 90°.
Solution.
Steps of construction:
1. Draw a line segment AB = 4 cm.
2. Take B as centre and draw an angle of 90°. Now take B as centre and draw an arc of 4 cm
which intersects the angle line at C.
3. Further at C draw 90° angle. From C take an arc of 4 cm and mark the point E.
4. Finally, by taking A as centre, draw an arc of 5 cm which will cut the produced line CE at

3. D. Join DA, AE.
5. Hence, ABCD is the required trapezium.