GEOMETRY HOMEWORK.pdf

7/27/2019 GEOMETRY HOMEWORK.pdf

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OMTEX CLASSES SIMILARITYASSIGNMENT

1. In fig 1.11

ABC = DCB = 900,

AB = 10 and DC = 15, find

A(ABC):A(DCB)

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 BPseg AC,

seg DQseg AC,

BP = 3, DQ = 5,

A(ABC) = 12

Find A(ADC)

4. In fig. 1.14, seg AD 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 area40. 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)

(ii) A(PAC):A(PAD)

(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 thecorresponding base of larger triangle.

8. In fig. 1.17

Seg AD is median ofABC, BD = 5,

then find (i) A(ABD): A(ADC)

(ii) A(ABD):A(ABC)

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 ofMNP, if MN = 7, NP = 10.5, MQ = 3, then find QP.

12. IfPQR ~ 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. IfABC ~MNP and BC:NP=3:4 then find A(ABC):A(MNP)

18. IfLMN ~ RST and A(LMN) = 100 sq. cm. A(RST) = 144 sq. cm. LM = 5cm, then find RS.19. IfABC ~ 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) = 16 A(PMN) then find QR: MN.


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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 9 cm, Find its side and perimeter.2

32. ABCD is a rhombus, AB = 20, AC = 24 , find BD.

33. Hypotenuse of an isosceles right angled triangle is 7 cm, Find the remaining sides of the triangle.2

34. PQRS is a parallelogram, Q = 600, seg PMside 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

Neelams house. then she turned to the north and travelled 4 km to Rosys house. Find the

straight distance between Nilofars and Rosys 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 triangle, the side opposite to angle 600 is 5 . Find the remaining sides.3

39. The sides of triangle are 11cm, 61 cm, and 60 cm. Determine whether the triangle is right angled .

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 = 13 , find the2

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 ofPQR.

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.

51. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

52. Prove that three times square of any side of an equilateral triangle is equal to four times the

square of an altitude.

53. Find the length of a altitude of an equilateral triangle each side measuring a units.

54. Find the side of a square whose diagonal is 16 cm.2

55. Find the perimeter of an isosceles right angled triangle with each of the congruent sides measuring 7cm.

56. The adjacent sides of a parallelogram are 11cm and 17 cm. If the length of one of its diagonals is26 cm, then find the length of the other diagonal.

57. If two circles touch externally, then show that the distance between their centres is equal to the sum

of their radii.

58. If two circles with radii 8 and 3 respectively touch internally, then show that the distance between


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their centres is equal to the difference of their radii. Find the distance between their centres.

MENSURATION ASSIGNMENT

1. The radius of a circle is 21 cm. Find (i) length of the arc (ii) area of the sector, when the corresponding central angle

are: (a) 600 (b) 750 (c) 1350

2. An arc of length 18 cm subtends an angle of 2700 at the centre. Find the radius and the area of the sector formed by

this arc.

3. The area of a sector of a circle is 207.9 sq. cm. and the measure of the arc of the sector is 54 0. Find (i) the radius of

the circle (ii) the length of the arc.

4. The circumference of a circle is 198 cm. The measure of the arc of the circle is 40 0. Find (i) the radius of the circle (ii)

area of the sector.

5. If the sector of a circle with radius 10 cm has central angle 180. find the area of the sector.

Answers: 1. (a) 22cm, 231 sq.cm. (b) 27.5 cm, 288.75 sq.cm. (c) 49.5 cm , 519.75 sq.cm.

2. Radius = 12 cm A(sector) = 108 sq. cm. 3. 21 cm, 19.8 cm. 4. 31.5 cm, 346.5 sq.cm. 5. 15.7 sq.cm.

CO - ORDINATE GEOMETRY ASSIGNMENT

SET A

1. Find the slope of the line passing through the following points. A(3,4) and B(-2,-1).

2. If A(6,1), B(0,-5), C(-8,-3)and D(-2,3) are the vertices ofABCD, Show that it is a parallelogram.

3. The vertices of a triangle are P( 1, -1) , Q (-1, 1) and R (-3, -2). Find the slope of each side of PQR.

4. Find the value of k, if the given points are collinear. A(4,11) B(2,5) C(6,k).

5. Find the value of k, if the slope of the line joining the points (2,10) and (k,4) is 3 / 4 .

Answers: (1) 1 (3) Slope of PQ = -1, Slope of QR = 3/2, Slope of PR = 1/4. (4) k = 17 (5) k = 1

SET B

1. Find the slope and y - intercept of the line: 2y=3x-6

2. Write the equation of the line if m = 2 and c = -5

3. Write the equation of the given line in slope-intercept form. 4x-3y+2=0.

4. If (10,5) is a point on the line 5x - 7y = c, find c.

5. If (-3,-2) is a point on the line 3y = mx-9, find m.

Answers: (1) Slope = 3/2, y-intercept = -3 (2) y = 2x-5 (3) y = +2/3 (4) c = 15 (5) m = -13

4x

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GEOMETRY HOMEWORK.pdf