#### 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 12: Isosceles Triangle

### Frank solutions for Class 9 Maths ICSE Chapter 12 Isosceles Triangle Exercise 12.1

Find the angles of an isosceles triangle whose equal angles and the non - equal angles are in the ratio 3: 4.

Find the angles of an isosceles triangle which are in the ratio 2:2:5.

Each equal angle of an isosceles triangle is less than the third angle by 15°. Find the angles.

Find the interior angles of the following triangles:

Find the interior angles of the following triangles:

Find the interior angles of the following triangles:

Find the interior angles of the following triangles:

Side BA of an isosceles triangle ABC is produced so that AB = AD. If AB and AC are the equal sides of the isosceles triangle, prove that ∠BCD is a right angle.

The bisector of the equal angles of an isosceles triangle PQR meet at O. If PQ = PR, prove that PO bisects ∠P.

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

DPQ is an isosceles triangle with DP = DQ. A straight line CD bisects the exterior ∠QDR. Prove that DC is parallel to PQ.

In a quadrilateral PQRS, PQ = PS and RQ = Rs. If ∠50° and ∠R = 110°, find ∠PSR.

ΔABC is an isosceles triangle with AB = AC. Another triangle BDC is drawn with base BC = BD in such a way that BC bisects ∠B. If the measure of ∠BDC is 70°, find the measures of ∠DBC and ∠BAC.

ΔPQR is isosceles with PQ = PR. T is the mid-point of QR, and TM and TN are perpendiculars on PR and PQ respectively. Prove that,

TM = TN

ΔPQR is isosceles with PQ = PR. T is the mid-point of QR, and TM and TN are perpendiculars on PR and PQ respectively. Prove that,

PM = PN

ΔPQR is isosceles with PQ = PR. T is the mid-point of QR, and TM and TN are perpendiculars on PR and PQ respectively. Prove that,

PT is the bisector of ∠P.

ΔPQR is isosceles with PQ = QR. QR is extended to S so that ΔPRS becomes isosceles with PR = PS. Show that ∠PSRSP : ∠QPS = 1 : 3

In ΔKLM , KT bisects ∠LKM and KT = TM. If ∠LTK is 80°, find the value of ∠LMK and ∠KLM.

Equal sides QP and RP of an isosceles ΔPQR are produced beyond P to S and T such that ΔPST is an isosceles triangle with PS = PT. Prove that TQ = SR.

Prove that the bisector of the vertex angle of an isosceles triangle bisects the base perpendicularly.

In the figure ΔABC is isosceles with AB = AC. Prove that:

∠A : ∠B = 1 : 3

In the figure ΔABC is isosceles with AB = AC. Prove that:

∠ADE = ∠BCD

In ΔABC, D is the mid-point of BC, AD is equal to AC. AC is produced to E, such that CE = AC. Prove that:

∠ADB = ∠DCE

In ΔABC, D is the mid-point of BC, AD is equal to AC. AC is produced to E, such that CE = AC. Prove that:

AB = CE

In ΔXYZ, AY and AZ are the bisector of ∠Y and ∠Z respectively. The perpendicular bisectors of AY and AZ cut YZ at B and C respectively. Prove that line segment YZ is equal to the perimeter of ΔABC.

ΔPQR is an isosceles triangle with PQ = PR. QR is extended to S and ST is drawn perpendicular to QP produced, and SN is perpendicular to PR produced. Prove that QS bisects ∠TSN.

In the given figure, D and E are points on AB and AC respectively. AE and CD intersect at P such that AP = CP. If ∠BAE = ∠BCD, prove that DBDE is isosceles.

In DPQR as shown, ∠PQS = ∠RQS and QS ⊥ PR. Find the value of x and y, if PQ = 3x + 1; QR = 5y - 2; PS = x + 1 and SR = y + 2.

In the given figure :

if ∠PQS = 60°,

find∠QPR.

In the given figure :

if ∠PQS = 60°,

show that PQ = PS = QS = SR.

In the give figure, if DPQR is an isosceles triangle, prove that: ∠QSR = exterior ∠PRT.

In the given figure, if DABC is an isosceles triangle and ∠PAC = 110^{o}, find the base angle and vertex angle of the DABC.

## Chapter 12: Isosceles Triangle

## Frank solutions for Class 9 Maths ICSE chapter 12 - Isosceles Triangle

Frank solutions for Class 9 Maths ICSE chapter 12 (Isosceles Triangle) 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 12 Isosceles Triangle are Isosceles Triangles, Isosceles Triangles : If Two Sides of a Triangle Are Equal, the Angles Opposite to Them Are Also Equal., Isosceles Triangle : If Two Angles of a Triangle Are Equal, the Sides Opposite to Them Are Also Equal..

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