ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 1.
In the given figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 2.
In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AC, show that PM × PC = PN × PB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 3.
(a) In the figure (1) given below. ∠AED = ∠ABC. Find the values of x and y.
(b) In the fig. (2) given below, CD = \(\\ \frac { 1 }{ 2 } \) AC, B is mid-point of AC and E is mid-point of DF. If BF || AG, prove that:
(i) CE || AG
(ii) 3ED = GD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 4.
In the given figure, 2AD = BD, E is mid-point of BD and F is mid-point of AC and EC || BH. Prove that:
(i) DF || BH
(ii) AH = 3AF.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 5.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 6.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and AC = 8.8cm. Is DE || BC? Justify your answer.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 7.
In a ∆ABC, DE is parallel to the base BC, with D on AB and E on AC. If \(\frac { AD }{ DB } =\frac { 2 }{ 3 } ,\frac { BC }{ DE } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 8.
If the area of two similar triangles are 360 cm² and 250 cm² and if one side of the first triangle is 8 cm, find the length of the corresponding side of the second triangle.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 9.
In the adjoining figure, D is a point on BC such that ∠ABD = ∠CAD. If AB = 5 cm, AC = 3 cm and AD = 4 cm, find
(i) BC
(ii) DC
(iii) area of ∆ACD : area of ∆BCA.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 10.
In the adjoining figure, the diagonals of a parallelogram intersect at O. OE is drawn parallel to CB to meet AB at E, find the area of DAOE : area of ||gm ABCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 11.
In the given figure, ABCD is a trapezium in which AB || DC. If 2AB = 3DC, find the ratio of the areas of ∆AOB and ∆COD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 12.
In the adjoining figure, ABCD is a parallelogram. E is mid-point of BC. DE meets the diagonal AC at O and meets AB (produced) at F. Prove that
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test
(i) DO : OE = 2 : 1
(ii) area of ∆OEC : area of ∆OAD = 1 : 4.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

Question 13.
A model of a ship is made to a scale of 1 : 250. Calculate :
(i) the length of the ship, if the length of the model is 1.6 m.
(ii) the area of the deck of the ship, if the area of the deck of the model is 2.4 m².
(iii) the volume of the model, if the volume of the ship is 1 km³.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths

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