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WORKSHEET 8 SIMILAR TRIANGLES

Published by Ratul Pal, 2021-10-25 07:51:40

Description: WORKSHEET 8 SIMILAR TRIANGLES

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TERM – 1 WORKSHEET – 8 SIMILAR TRIANGLES CRITERIA FOR SIMILARITY OF TRIANGLES AA OR AAA SIMILARITY CRITERION: SAS SIMILARITY CRITERION: BASIC PROPORTIONALITY THEOREM( or THALES THEOREM)

CONVERSE OF BASIC PROPORTIONALITY THEOREM SSS SIMILARITY CRITERION:

RHS SIMILARITY CRITERION: PYTHAGORAS THEOREM: 1. If in ∆ ������������������ ������������������ ∆������������������, ������������ = ������������, then they will be similar, when ������������ ������������ a) ∠������ = ∠������ c) ∠������ = ∠������ b) ∠������ = ∠������ ������) ∠������ = ∠������ 2. In the figure DE ∥ BC . If AD = x, DB = x - 2, AE = x + 2 and EC = x -1, then the value of x is

a) 9 b) 4 c) 4.5 d) 8 3. In the given figure of ∆ ������������������, ������������ ∥ ������������. If DC ∥ AP, where point P lies on BC produced, then ������������ = ������������ a) ������������ b) ������������ c) ������������ d) None of these ������������ ������������ ������������ 4. In ∆ ������������������, D and E are points on the sides AB and AC respectively, such that DE BC. If AD = 4x – 3 , AE = 8x – 7, BD = 3x – 1 and CE = 5x – 3, then the value of x is a) 1 b) 4 c) 1 d) 2 23 5. In ∆ ������������������, ������������ ∥ ������������, ������������ = 3 and PR = 28cm, then the value of PT is ������������ 5 a) 9.5 cm b) 9cm c) 10cm d) 10.5cm

6. In the given figure , if AB∥ CD, then the value of x is a) 6 b) 8 c) 3 d) 9 7. The line joining the mid – points of two sides of a triangles is a) Bisector of the third side b) Perpendicular to the third side c) Parallel to the third side d) None of these 8. In the adjoining figure, ������������ = ������������ and ∠PST = ∠PRQ. Then, ∆PQR is an ������������ ������������ a) Equilateral triangle b) Right angled triangle c) Isosceles triangle d) Can’t say 9. In ∆ ������������������ ������������������ ∆������������������ , ∠B = ∠E, ∠F = ∠������ and AB = 3DE. Then, the two triangles are a) Congruent but not similar b) Similar but not congruent c) Neither congruent nor similar d) Congruent as well as similar 10. The value of the height ‘h’ in the adjoining figure is, at which the tennis ball must be hit, so that it will just pass over the net and land 6 m away from the base of the net

a) 3.6m b) 3m c) 2.7m d) 0.27 m 11.In the given figure, ∆ODC ~∆OBA. ∠BOC = 125° and ∠CDO = 70° , then the value of ∠OAB is a) 70° b) 125° c) 65° d) 55° 12. A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is a) 100m b) 120m c) 25 m d) 200 m 13.A girl of height 90 cm is walking away from the base of a lamp – post at a speed of 1.2 m/s . If the lamp is 3.6m above the ground, then the value of length of her shadow after 4s is a) 3.2 m b) 4.8 m c) 1.6 m d) 3.6 m 14. A flag pole 18 m high casts a shadow 9.6 m long. Then, the distance of the top of the pole from the far end of the shadow is a) 18 m b) 26 m c) 21 m d) 20.4 m 15. It is given that ∆ABC ~ ∆ DEF, ∠A = 30°, ∠C = 50°, AB = 5cm, AC = 8cm and DF = 7.5 cm. Then, which of the following is true? a) DE = 12 cm ∠F = 50° b) DE = 12 cm ∠F = 100° b) EF = 12 cm ∠D = 100° d) EF = 12 cm ∠D = 30°

16. In figure two line segments AC and BD intersect each other at the point Psuch that PA = 6cm, PB = 3cm, PC = 2.5 cm , PD = 5 cm , ∠APB = 50° and ∠CDP = 30°. Then , ∠PBA is equal to a) 50° b) 30° c) 60° d) 100° 17.If ∆ABC ~∆QRP, ������������(∆������������������) 9 , AB = 18 cm and BC = 15cm, then PR is equal ������������(∆������������������) 4 to a) 10 cm b) 12 cm c) 20 ������������ d) 8cm 3 18. In ∆ABC and ∆RPQ, AB = 4.5 cm, BC = 5 cm, CA = 6√2 cm, PR = 12√2 cm, PQ = 10cm, QR = 9 cm. If ∠A = 75° and ∠B = 55° , then ∠P is equal to a) 75° b) 55° c) 50° d) 130° 19. In ∆PQR ~ ∆XYZ and ������������ = 52, then ������������(∆������������������) is equal to ������������ ������������(∆������������������) a) 4 b) 2 c) 25 d) 5 25 5 4 2 20.∆ABC and ∆BDE are two equilateral triangles such that D is the mid - point of BC. Ratio of the area of triangles ABC and BDE is a) 2:1 b) 1:2 c) 1:4 d) 4:1 21. If Manish goes 3 Km towards East and then 4 Km towards North. His distance from starting point is a) 3 Km b) 4 Km c) 5 Km d) 2 Km 22.It is given that ∆ABC ~∆PQR , with ������������ = 31. Then , ������������(∆������������������) is equal to ������������ ������������(∆������������������) a) 9 b) 3 c) 1 d) 1 3 9 23.If S is a point on side PQ of a ∆PQR such that PS = QS =RS, then a) PR.QR=RS2 B) QS2+RS2 = QR2 c) PR2 + QR2 = PQ2 d) PS2+RS2=PR2 24. In a ∆ABC , ∠A = 25, ∠B = 35 and AB = 16 units. In ∆PQR, ∠P = 35°. ∠Q = 120° and PR = 4 units. Which of the following is true? a) ������������(∆������������������) = 2������������(∆������������������) b) ������������(∆������������������) = 4������������(∆������������������)

b) ������������(∆������������������) = 8������������(∆������������������) d) ������������(∆������������������) = 16������������(∆������������������) 25. A ∆������������������ is similar to another triangle ABC such that ar(∆������������������) = 4 (∆������������������). The ratio of their perimeter is given as a) 2:1 b) 1:2 c) 4:1 d) None of these 26. The areas of two similar triangles are 144cm2 and 81cm2. If one median of the first triangle is 16 cm, length of corresponding median of the second triangle is a) 9 cm b) 27cm c) 12 cm d) 16 cm 27.If in two triangles ABC and DEF, ������������ = ������������ = ������������ then ������������ ������������ ������������ a) ∆ABC ~ ∆DEF b) ∆ABC ~ ∆EDF c) ∆ABC ~ ∆EFD d) ∆ABC ~ ∆DFE 28. Vatsal claims that congruent figures are similar as well. Vinayak claims that similar figures are congruent as well. Who is/are correct? a) Only Vatsal b) only Vinayak c) both vatsal and Vinayak d) neither Vatsal nor Vinayak 29.Two quadrilaterals are such that their diagonals bisect each other. What additional information is required to conclude that the quadrilaterals are similar? a) Opposite angles are equal b) Opposite sides are equal c) Diagonals bisect at right angle and adjacent angles are equal d) Diagonals are equal and opposite sides are equal 30.Consider the figure below.

Which of the following statement is correct about the triangles in the figure? a) ∆AOB ~ ∆DOC because ������������ = ������������ ������������ ������������ b) ∆AOB ~ ∆DOC because ������������ = ������������ and ∠������������������ = ∠������������������ ������������ ������������ c) ∆AOB ~ ∆DOC because ������������ = ������������ and ∠������������������ = ∠������������������ ������������ ������������ d) ∆AOB ~ ∆DOC because ∠������������������ = ∠������������������ 31. Consider the figure below. Which of the following statement help proving that triangle ABO is similar to triangle DOC? (i) ∠B = 70° and (ii) ∠C = 70° a) Statement ( i) alone is sufficient, but statement (ii) alone is not sufficient. b) Statement ( ii) alone is sufficient, but statement (i) alone is not sufficient c) Each statement alone is sufficient. d) Both statement together is sufficient, but neither statement alone is sufficient 32. In the figure below, PQ ∥ CB.

To the nearest tenth, what is the length of QB? a) 1.4 cm b) 1.7 cm c) 1.8 cm d) 2.2 cm 33. In the given figure , QR ∥ AB , RP ∥ BD, CQ = x + 2, QA = x, CP = 5x +4, PD = 3x. The value of x is……. . a) 1 b) 6 c) 3 d) 9 34. Rohit is 6 feet tall. At an instant, his shadow is 5 feet long. At the same instant, the shadow of a pole is 30 feet long. How tall is the pole? a) 12 feet b) 24 feet c) 30 feet d) 36 feet 35.Ankit is 5 feet tall. He places a mirror on the ground and moves until he can see the top of a building. At the instant when Ankit is 2 feet from the mirror, the building is 48 feet from the mirror. How tall is the building? a) 96 feet b) 120 feet c) 180 feet d) 240 feet 36. The area of two similar triangles are a and k2a. What is the ratio of the corresponding side lengths of the triangles? a) 1:k b) 1:k2 c) 1:a d) 1:a2 37. In the figure below, PQ ∥ BC.

The ratio of the perimeter of triangle ABC to the perimeter of Triangle APQ is 3:1. Given that the numerical value of the area of triangle APQ is a whole number, which of the following could be the area of the triangle ABC? a) 28 b)60 c) 99 d) 120 38.The ratio of the areas of two similar triangles , ABC and PQR shown below is 25:144. What is the ratio of their medians AM and PN? a) 5:12 b) 5:16 c) 12:5 d) 25 :144 39.The ratio of the areas of two similar right triangle is 9:16. The length of one of the sides of the smaller triangle is 15 cm. How much longer is the length of the corresponding side of the larger triangle from smaller triangle? a) 2cm b) 3 cm c) 4 cm d) 5 cm 40.Observe the right triangle ABC, right angled at B as shown below.

What is the length of PC? a) 2.5cm b) 4.5 cm c) 6 cm d) 7.5 cm 41.Observe the right triangle ABC, right angled at A as shown below. If BP ⊥ AC, then which of the following is NOT correct? a) ∆APB ~ ∆ABC b) ∆APB ~ ∆BPC C) BC2 = CP.AC d)AC2 = AB.CB 42.Consider the figure below. Mr shah follows the below step to prove AB2+BC2=AC2. (i) ∆APB ~ ∆ABC (ii) ������������ = ������������ (iii) AB2=AP.AC ������������ ������������ Which of these could be his next step? (a) Prove ∆ABC ~ ∆PAB (b) Prove ∆BPC ~ ∆ABC (c) Prove ∆APB ~ ∆BPC (d) Prove ∆APB ~ ∆������PB 43. In figure , ABC is an isosceles triangle, right – angled at C. Therefore

a) AB2 = 2AC2 b) BC2= 2AB2 c) AC2 = 2 AB2 d) AB2=4AC2


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