# 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.

## Chapter 16 - Similarity Exercise Ex. 16.1

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'.

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

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

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

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.

## Chapter 16 - Similarity Exercise Ex. 16.2

Given that name the corresponding angles and the corresponding sides.

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

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.

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

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?

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'

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