Class 9 Maths Important Questions for Constructions
Given below are the Class 9 Maths Important Questions for Constructions
a. Multiple Choice Questions
b. Long answer questions
c. True and False
Construction Question
1. Construct a triangle ABC, in which <B = 60°, <C = 45° and AB + BC + CA = 11cm
2. Construct a triangle XYZ in which <Y = 30°, <Z = 90° and XY + YZ + ZX = 11cm
3. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.
4. Construct a triangle PQR whose perimeter is equal to 14 cm, <P =45° and <Q = 60°.
5. Using ruler and compasses only, construct a ABC from the following data:
AB + BC + CA = 12 cm, <B = 45° and <C = 60°
6. Using ruler and compasses only, construct a ABC given base BC = 7 cm, <ABC = 60° and AB + AC = 12 cm.
7. Construct a right angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60°.
8. Construct a triangle XYZ in which <Y = 30°, >Z = 90° and XY + YZ + ZX = 11.
9. Construct a ABC with BC = 8cm, <B = 45° and AB – AC = 31cm.
10. Construct a triangle ABC in which BC = 4.7 cm, AB + AC = 82 cm and <C = 60°.
11. Construct a ABC such that BC = 3.2 cm, <B = 45° and AC – AB = 2.1 cm.
12. Construct an isosceles triangle whose two equal sides measures 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex.
13. To construct a triangle, with perimeter 10 cm and base angles 60 and 45.
14. Construct an equilateral triangle with one side 6 cm.
15. Construct a ABC in which BC = 4.5 cm, <B = 60° and AB = AC = 7.1 cm.
16. Construct a ABC in which BC = 7.5 cm, <B = 45° and AB – AC = 4 cm.
17. Construct a ABC in which BC = 8.5 cm, AB = 7 cm and median AD = 4.8 cm.
18. Construct a right triangle whose perimeter is 10 cm and one of its acute angle is equal to 60°.
19. Construct a rhombus whose diagonals are 4 cm and 6 cm in length.
20. Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm.
21. Construct a right triangle whose one side is 8 cm and sum of other sides and hypotenuse is 16 cm.
22. Construct an isosceles triangle LM, whose base MN is 4.5 cm and the sum of the perpendicular from L to MN and LM is 7 cm.
23. Draw a right angled whose hypotenuse is 6 cm and the length of one of whose sides containing the right angle is 4 cm.
24. Construct an equilateral PQR is its altitude is 4 cm.
25. Draw a PQR with base QR = 6 cm and angles in the ratio 3 : 4 : 5.
26. Construct a triangle PQR whose sides are 3.6 cm, 3.0 cm and 4.8 cm. bisect the smallest angle and measure its each part.
27. Draw an angle of 110° with help of a protector and bisect it. Measure angle.
True and False
28. Write True or False in each of the following. Give reasons for your answer:
a. An angle of 52.5° can be constructed with the help of a ruler and a compass.
b. An angle of 42.5° can be constructed with the help of a ruler and a compass.
c. A triangle ABC can be constructed in which AB = 5 cm, $\angle A = 45$° and BC + AC = 5 cm.
d. A triangle ABC can be constructed in which BC = 6 cm, $\angle C = 30$° and AC � AB = 4 cm.
e. A triangle ABC can be constructed in which $ \angle B = 105$°, $\angle C = 90$° and AB + BC + AC = 10 cm.
f. A triangle ABC can be constructed in which $\angle B = 60$°, $\angle C = 45$° and AB + BC + AC =12 cm.
Multiple Choice questions
29. With the help of a ruler and a compass, it is possible to construct an angle of :
(A) 35°
(B) 40°
(C) 37.5°
(D) 47.5°
30. The construction of a triangle ABC in which AB = 4 cm, <A = 60° is not possible when difference of BC and AC is equal to:
(A) 3.5 cm
(B) 4.5 cm
(C) 3 cm
(D) 2.5 cm
31. The construction of a triangle ABC, given that BC = 6 cm, <B = 45° is not possible when difference of AB and AC is equal to:
(A) 6.9 cm
(B) 5.2 cm
(C) 5.0 cm
(D)4.0 cm
Answer
28.
a.True. As 52.5° =210/4 and 210° =180°+ 30° which can be constructed.
b. False. As 42.5° =85/2 and 85° cannot be constructed.
c. False. As BC + AC must be greater than AB which is not so.
d. True. As AC � AB < BC, i.e., AC < AB + BC.
e. False. As <B + <C = 105° + 90° = 195° >180°.
f. True. As <B + <C = 60° + 45° = 105� < 180°
29. Solution : Answer (C)
30. Solution : Answer (B)
31. Solution : Answer (A)
