∟ABC = ∟DCB = 900,
AB = 10 and DC = 15, find
2. In the fig. 1.12
∟ABD = ∟BDC = 900 ,
A(∆ABD):A(∆BDC) = 4:5
If AB = 6 find DC.
3. In fig. 1.13.
seg BP 丄seg AC,
seg DQ 丄seg AC,
BP = 3, DQ = 5,
A(∆ABC) = 12
4. In fig. 1.14, seg AD 丄seg BC,
BD: DC = 3:5 then
Find: (i) A(∆ABD) : A(∆ADC)
(ii) A(∆ABD): A(∆ABC)
5. In fig. 1.15, line m || line n,
(i) A(∆ABD) = 40, Name the other triangle having area 40. Justify your answer.
(ii) A(∆DCA) = 30, Name another triangle having area having area 30. Justify your answer.
6. In the fig. 1.16,
if AB = 2, BC = 4, CD = 3 then find
(i) A(∆PAB) : A(∆PBC)
(iii) A(∆PAC) : A(∆PBD)
7. The ratio of the areas of triangles
having same height is 3:4. Base of the
smaller triangle is 15 cm. Find the corresponding base of larger triangle.
8. In fig. 1.17
Seg AD is median of ∆ABC, BD = 5,
then find (i) A(∆ABD): A(∆ADC)
9. According to information given in the
fig. 1.18 find x if line PQ || side BC.
10. ∆ABC and ∆PQR have same base and their corresponding heights are 5 and 3.5 units.
Find A(∆ABC) : A(∆PQR).
11. In ∆MNP, ray NQ is angle bisector of ∟MNP, if MN = 7, NP = 10.5, MQ = 3, then find QP.
12. If ∆PQR ~ ∆XYZ and PQ = 12, QR = 8, PR = 15, XY = 18, ∟P = 800 then find YZ, XZ and ∟X.
13. The sides of the triangular fields are 300 m, 200 m, and 150 m. In the map of this field, the longest side is shown as 6 cm in length. Find length of remaining sides in the map. (Hint: The field and its map are similar. Map ia a reduction of field.)
14. A man and his son are standing in open ground, their shadows are seen. The lengths of their shadows are found fo be 3m and 2.5 m, If height of his son is 1.5m, find the height of the man. (Hint: the triangles formed are similar.)
15. ∆DEF and ∆PQR are equilateral triangles justify that ∆DEF ~∆PQR.
16. Area of two similar triangles are 64 cm2 and 36cm2 .. If one side of the larger triangle is 12 cm then find the
corresponding side of the smaller triangle.
17. If ∆ABC ~∆MNP and BC:NP=3:4 then find A(∆ABC):A(∆MNP)
18. If ∆LMN ~ ∆RST and A(∆LMN) = 100 sq. cm. A(∆RST) = 144 sq. cm. LM = 5cm, then find RS.
19. If ∆ABC ~ ∆PQR and A(∆ABC) = 81 cm2. If AB = 6 cm, PQ = 12cm, then find A(∆PQR) .
20. Areas of two similar triangles are 225 cm2 and 81 cm2 . If one side of the smaller triangle is 12 cm, then find the corresponding side of the larger triangle.
21. ∆PQR ~ ∆PMN and if 9 A(∆PQR) = 16A(∆PMN) then find QR: MN.
22. ∆ABC and ∆PQR are equilateral triangles AB = 8 cm and PQ = 6 cm, then find A(∆ABC) : A(∆PQR).
23. Two similar triangles have same area, then find the ratio of their corresponding sides.
24. The shadow of pole of height 2m and a tree of certain height are seen on the plane ground. Their length is were found to be 3m and 5.7 m respectively, then find the height of tree.
25. A, B and C are three villages, distance between villages A and B is 72 km, the distance between the villages B and C is 80 km and that between villages C and A is 64 km. In a map, if the distance between villages A and B is shown as 9 cm. then draw the map with proper scale.
26. In a right angled triangle , the sides forming right angle are 12 cm and 16 cm. Find the hypotenuse.
27. Find the diagonal of a rectangle having length of sides 9 and 40.
28. Find the diagonal of a square having side 20 cm.
29. The hypotenuse and height of a right angled triangle is 25 cm and 15 cm respectively. Find the base of the triangle.
30. The lengths of sides of triangles are given below. Determine whether the tringle is right angled triangle.
i. a = 3, b = 5, c = 4 ii. x = 12, y = 15, z = 13 iii. p = 7, q = 8, r = 15. iv. l = 9, m = 40, n = 41 v. c = 25, d = 15, e = 15
31. Diagonal of a square is 92 cm, Find its side and perimeter.
32. ⃕ABCD is a rhombus, AB = 20, AC = 24 , find BD.
33. Hypotenuse of an isosceles right angled triangle is 72cm, Find the remaining sides of the triangle.
34. ⃕PQRS is a parallelogram, ∟Q = 600, seg PM 丄side QR. PQ = 8cm. Find PM and QM.
35. Nilofar started on a bicycle from her house. She went 3 km to the east and reached Neelam’s house. then she turned to the north and travelled 4 km to Rosy’s house. Find the straight distance between Nilofar’s and Rosy’s house.
36. Find the diagonal of a square having side 10cm.
37. ∆RPS is a 450 - 450 - 900 triangle. ∟RPS = 900. If RP = 7 cm, find RS.
38. In a 300 - 600 - 900 tringle, the side opposite to angle 600 is 53. Find the remaining sides.
39. The sides of triangle are 11cm, 61 cm, and 60 cm. Determine whethher the triangle is right angled triangle.
40. In a right angled triangle, if the hypotenuse is 25cm and base is 24 cm. Find its height and perimeter.
41. In a right angled ∆XYZ, ∟Y = 900 , side XY is congruent to side YZ. If XY = 132, find the length of the congruent sides.
42. ⃕PQRS is a rhombus having side 10cm. If PR = 16, then find QS.
43. In ∆PQR, ∟Q = 900 , ∟P = 600, ∟R = 300 . If PR = 20, then find PQ and QR.
44. The ratio of the areas of two triangles with the common base is 6:5. The height of the larger triangle is 9cm. Find the corresponding height of the smaller triangle.
45. ∆ABC has sides of length 5, 6 and 7 units. ∆PQR has perimeter 360 units. ∆ABC is similar to ∆PQR. Find the sides of ∆PQR.
46. A vertical pole of length 6m casts a shadow 4m long on the ground. At the same time a tower casts a shadow 28m long. Find the height of the tower.
47. The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas.
48. the ratio of two similar triangles are 81 sq. cm and 49 sq. cm. respectively. Find the ratio of their corresponding heights. What is the ratio of their corresponding medians?
49. The sides of triangles are given below. Determine which of them are right angled triangles:
i. 8, 15, 17 ii. 9, 40, 41 iii. 40, 20, 30 iv. 11, 60, 61 v. 11, 12, 15 vi. 12, 35, 37
50. A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall.