#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 16: Similarity

### Frank solutions for Class 9 Maths ICSE Chapter 16 Similarity Exercise 16.1

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.

If AD = 4, AE = 8, DB = x - 4 and EC = 3x - 19, find x.

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.

If AD : BD = 4 : 5 and EC = 2.5cm, find AE.

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.

If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3,Find x.

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.

If AD = 8cm, AB = 12cm and AE = 12cm, find CE.

If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:

AB = 5.6cm, AD = 1.4cm, AC = 7.2cm, and AE = 1.8cm

If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:

AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm

If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:

AD = 5.7cm, BD = 9.5cm, AE = 3.3cm, and EC = 5.5cm

In figure, PQ is parallel to BC, AP : AB = 2 : 7. If QC = 0 and BC = 21,

Find

(i) AQ

(ii) PQ

In ΔABC, DE is parallel to BC and DE = 3:8.

Find:

(i) AD : BD

(ii) AE, if AC = 16.

In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"EC"`

In ΔABC, point D divides AB in the ratio 5:7, Find: `"AD"/"AB"`

In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"AC"`

In ΔABC, point D divides AB in the ratio 5:7, Find: BC, If DE = 2.5cm

In ΔABC, point D divides AB in the ratio 5:7, Find: DE, If BC = 4.8cm

If ΔPQR, AB is drawn parallel to QR. If PQ = 9cm, PR = 6cm and PB = 4.cm, find the length of AP.

In ΔABC, MN is drawn parallel to BC. If AB = 3.5cm, AM : AB = 5 : 7 and NC = 2cm, find:

(i) AM

(ii) AC

The sides PQ and PR of the ΔPQR 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'.

ΔABC is right angled at A. AD is drawn perpendicular to BC. If AB = 8cm and AC = 6cm, calculate BD.

In the figure, PR || SQ. If PR = 10cm, PT = 5cm, TQ = 6cm and ST = 9cm, calculate RT and SQ.

ABCD is a parallelogram whose sides AB and BC are 18cm and 12cm respectively. G is a point on AC such that CG : GA = 3 : 5 BG is produced to meet CD at Q and AD produced at P. Prove that ΔCGB ∼ ΔAGP. Hence, fi AP.

In ΔABC, BP and CQ are altitudes from B and C on AC and AB respectively. BP and CQ intersect at O. Prove that

(i) PC x OQ = QB x OP

(ii) `"OC"^2/"OB"^2 = ("PC" xx "PO")/("QB" xx "QO")`

In the figure, PQR is a straight line and PS || RT. If QS = 12cm, QR = 15cm, QT = 10cm and RT = 6cm, find PQ and PS.

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where P is any point on side AB. Prove that CQ x PQ = QA x QD.

AM and DN are the altitudes of two similar triangles ABC and DEF. Prove that: AM : DN = AB : DE.

Prove that the external bisector of an angle of a triangle divides the opposite side externally n the ratio of the sides containing the angle.

In the figure, AB || RQ and BC || SQ, prove that `"PC"/"PS" = "PA"/"PR"`.

In the figure, DE || AC and DC || AP. Prove that `"BE"/"EC" = "BC"/"CP"`

PQ is perpendicular to BA and BD is perpendicular to AP.PQ and BD intersect at R. Prove that ΔABD ∼ ΔAPQ and `"AB"/"AP" = "BD"/"PQ"`.

Through the vertex S of a parallelogram PQRS, a line is drawn to intersect the sides Qp and QR produced at M and N respectively. Prove that `"SP"/"PM" = "MQ"/"QN" = "MR"/"SR"`

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 ΔPTQ - 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 of ABC and ABC =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.

### Frank solutions for Class 9 Maths ICSE Chapter 16 Similarity Exercise 16.2

Given that ΔABC ∼ ΔPRQ, name the corresponding angles and the corresponding sides.

In ΔABC, DE || BC 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?

The areas of two similar triangles are 16cm^{2} and 9cm^{2} respectively. If the altitude of the smaller triangle is 1.8cm, find the length of the altitude corresponding to the larger triangle.

The areas of two similar triangles are 169cm^{2} and 121cm^{2} respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.

D and E are points on the sides AB and AC of ΔABC such that DE | | BC and divides ΔABC into two parts, equal in area. Find `"BD"/"AB"`.

In ΔABC, DE is drawn parallel to BC cutting AB in the ratio 2 : 3. Calculate:

(i) `("area"(Δ"ADE"))/("area"(Δ"ABC")`

(i) `("area"("trapeziumEDBC"))/("area"(Δ"ABC"))`

In ΔABC, AB = 8cm, AC = 10cm and ∠B = 90°. P and Q are the points on the sides AB and AC respectively such that PQ = 3cm ad ∠PQA = 90. Find: The area of ΔAQP.

In ΔABC, AB = 8cm, AC = 10cm and ∠B = 90°. P and Q are the points on the sides AB and AC respectively such that PQ = 3cm ad ∠PQA = 90. Find: Area of quadrilateral PBCQ: area of ΔABC.

Find the scale factor in each of the following and state the type of size transformation:

Image length = 6cm, Actual length = 4cm.

Find the scale factor in each of the following and state the type of size transformation:

Actual length = 12cm, Image length = 15cm.

Find the scale factor in each of the following and state the type of size transformation:

Image length = 8cm, Actual length = 20cm.

Find the scale factor in each of the following and state the type of size transformation:

Actual area = 64m^{2}, Model area = 100cm^{2}

Find the scale factor in each of the following and state the type of size transformation:

Model area = 75cm^{2}, Actual area = 3cm^{2}

Find the scale factor in each of the following and state the type of size transformation:

Model volume = 200cm^{3}, Actual volume = 8cm^{3}

ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm

ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate: Length of AB, if A'B' = 5.4cm

ΔABC is enlarged, with a scale factor 5. Find: A'B', if AB = 4cm

ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm

ΔXYZ is enlarged to ΔX'Y'Z'. If XY = 12cm, YZ = 8cm and XZ = 14cm and the smallest side of ΔX'Y'Z' is 12cm, find the scale factor and use it to find the length of the other sides of the image ΔX'Y'Z'.

On a map drawn to a scale of 1: 2,50,000, a triangular plot of land has the following measurements:

AB = 3 cm, BC = 4 cm, ∠ABC = 90°. Calculate:

(i) The actual length of AB in km.

(ii) The area of Plot in sq. km.

The dimensions of the model of a building are 1.2m x 75cm x 2m. If the scale factor is 1 : 20; find the actual dimensions of the building.

The scale of a map is 1 : 50000. The area of a city is 40 sq km which is to be represented on the map. Find: The area of land represented on the map.

The scale of a map is 1 : 50000. The area of a city is 40 sq km which is to be represented on the map. Find: The length of a scale in km represented by 1cm on the map.

A plot of land of area 20km^{2} is represented on the map with a scale factor of 1:200000. Find: The number of KM represented by 2cm on the map.

A plot of land of area 20km^{2} is represented on the map with a scale factor of 1:200000. Find: The ground area in km^{2 }that is represented by 2cm^{2} on the map.

A plot of land of area 20km^{2} is represented on the map with a scale factor of 1:200000. Find: The area on the map that represented the plot of land.

A map is drawn to scale of 1:20000. Find: The distance covered by 6cm on the map

A map is drawn to scale of 1:20000. Find: The distance on the map representing 4km

A map is drawn to scale of 1:20000. Find: The area of the lake on the map which has an actual area of 12km^{2}

A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The length of the truck

A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The volume of the model if the volume of the truck is 6m^{3}

A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The base area of the truck, if the base area of the model is 30m^{2}

A model of a ship is made to a scale of 1:500. Find: The length of the ship, if length of the model is 1.2.

A model of a ship is made to a scale of 1:500. Find: The area other deck o the ship, if the area of the deck of its model is m^{2}

A model of a ship is made to a scale of 1:500. Find: The volume of the model when the volume of the ship is 1km^{3 }

On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km

On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The area of the plot in sq km

On a map drawn to a scale of 1:25000, a triangular plot of land is right angled and the sides forming the right angle measure 225cm and 64cm.Find: The actual length of the sides in km

On a map drawn to a scale of 1:25000, a triangular plot of land is right angled and the sides forming the right angle measure 225cm and 64cm.Find: The area of the plot in sq. km.

In a triangle ABC, AB = 4 cm, BC = 4.5 cm and CA = 5 cm. Construct ΔABC. Find the image A'B'C of the ΔABC 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'

## Chapter 16: Similarity

## Frank solutions for Class 9 Maths ICSE chapter 16 - Similarity

Frank solutions for Class 9 Maths ICSE chapter 16 (Similarity) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Maths ICSE chapter 16 Similarity are Figures Between the Same Parallels, Triangles with the Same Vertex and Bases Along the Same Line, Concept of Area, Similarity.

Using Frank Class 9 solutions Similarity exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.

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