# FRANK Solutions for Class 9 Maths Chapter 16 - Similarity

Revise the AA criterion for Similarity and the Basic Theorem of Proportionality with TopperLearning’s Frank solutions for ICSE Class 9 Mathematics Chapter 16 Similarity. Practising the solutions will help you grasp simple applications of various conditions of Similarity. Similarity-based problems won’t intimidate you if you put in efforts to learn and review the step-wise textbook solutions provided by our experts.

The Frank solutions for ICSE Class 9 Maths also shows you how to calculate the area of a triangle or a quadrilateral using the Pythagoras theorem. Revise Maths concepts from Chapter 16 with these solutions and other e-learning materials like online practice tests, video lessons, etc.

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## Chapter 16 - Similarity Exercise Ex. 16.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8

The sides PQ and PR of thePQR are produced to S and T respectively. ST is drawn parallel to QR and PQ: PS = 3:4. If PT = 9.6 cm, find PR. If 'p' be the length of the perpendicular from P to QR, find the length of the perpendicular from P to ST in terms of 'p'.

Solution 8

Question 9
Solution 9
Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21(a)

In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that

PTQ - DRTS

Solution 21(a)

Question 21(b)

In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that

TP:TQ = TR:TS

Solution 21(b)

Question 22(a)

In the given figure, PB is the bisector ofABC andABC =ACB. Prove that:

a. BC x AP = PC x AB

b. AB:AC = BP: BC

Solution 22(a)

Question 23

In a right-angled triangle ABC,B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.

Solution 23

## Chapter 16 - Similarity Exercise Ex. 16.2

Question 1

Given that name the corresponding angles and the corresponding sides.

Solution 1

Question 2

InBC such that AD =1.5 cm, DB = 3 cm and AE = 1 cm. Find AC.

Solution 2

Question 3

Given is a triangle with sides 3 cm, 5 cm and 6 cm. Find the sides of a triangle which is similar to the given triangle and its shortest side is 4.5 cm.

Solution 3

Question 4

Two figures are similar. If the ratio of their perimeters is 8:16. What will be the ratio of the corresponding sides?

Solution 4

Question 5

Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

In a triangle ABC, AB = 4 cm, BC = 4.5 cm and CA = 5 cm. ConstructABC. Find the image A'B'C of theABC obtained by enlarging it by a scale factor 2. Measure the sides of the image A'B'C' and show that

AB:A'B' = AC:B'C' = CA:C'A'

Solution 24

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