Isosceles Triangles Concise Class-9th Selina ICSE Maths

Isosceles Triangles Concise Class-9th Selina ICSE Mathematics Solutions Chapter-10 by RK Bansal .  We provide step by step Solutions of Exercise / lesson-10 Isosceles Triangles for ICSE Class-9 Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-10 A and Exe-10 B, to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics .

Isosceles Triangles Concise Class-9th Selina ICSE Mathematics Solutions Chapter-10  by R K Bansal.


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Exe-10 A,

Exe-10 B,

 


Exercise – 10 A, Isosceles Triangles Concise Class-9th Selina ICSE Mathematics Solutions by RK Bansal

Question 1

In the figure alongside,

……………

AB = AC

A = 48o and

Angel ACD = 18o.

Show that BC = CD.

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Answer

Ans 1 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 2

Calculate:

(i) ∠ADC

(ii) ∠ABC

(iii) ∠BAC

Answer

Ans 2 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 3

In the following figure, AB = AC; BC = CD and DE is parallel to BC. Calculate:

(i) ∠CDE

(ii) ∠ DCE

Answer

Ans 3 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

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Question 4

Calculate x:

(i)………………….

(ii)…………………….

Answer

Ans 4 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 5

In the figure, given below, AB = AC. Prove that: BOC = ACD.

Answer

Ans 5 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 6

In the figure given below, LM = LN; angle PLN = 110o. Calculate:

(i) ∠LMN

(ii) ∠MLN

Answer

Ans 6 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 7

An isosceles triangle ABC has AC = BC. CD bisects AB at D and CAB = 55o.

Find: (i) ∠DCB (ii) ∠CBD.

Answer

Ans 7 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 8

Find x:

…………………..

Answer

Ans 8 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 9

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

Answer

Ans 9 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 10

In the given figure; AE // BD, AC // ED and AB = AC. Find ∠a, ∠b and ∠c.

Answer

Ans 10 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 11

In the following figure; AC = CD, AD = BD and ∠C = 58o.

Find angle CAB.

Answer

Ans 11 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 12

In the figure of q. no. 11 given above, if AC = AD = CD = BD; find angle ABC.

Answer

Ans 12 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 13

In triangle ABC; AB = AC and ∠A : ∠B = 8 : 5; find angle A.

Answer

Ans 13 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 14

In triangle ABC; ∠A = 60o, ∠C = 40o, and bisector of angle ABC meets side AC at point P. Show that BP = CP.

Answer

Ans 14 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 15

In triangle ABC; angle ABC = 90o and P is a point on AC such that ∠PBC = ∠PCB. Show that: PA = PB.

Answer

Ans 15 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 16

ABC is an equilateral triangle. Its side BC is produced upto point E such that C is mid-point of BE. Calculate the measure of angles ACE and AEC.

Answer

Ans 16 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 17

In triangle ABC, D is a point in AB such that AC = CD = DB. If ∠B = 28°, find the angle ACD.

Answer

Ans 17 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 18

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. Find angle DAC.

Answer

Ans 18 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 19

Prove that a triangle ABC is isosceles, if:

(i)  altitude AD bisects angles BAC, or

(ii)  bisector of angle BAC is perpendicular to base BC.

Answer

Ans 19 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 20

In the given figure; AB = BC and AD = EC.

Prove that: BD = BE.

Answer

Ans 20 Exercise - 10 A Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions


Selina ICSE Mathematics Solutions, Isosceles Triangles Concise Class-9th Exercise – 10 B

Question 1

If the equal sides of an isosceles triangle are produced, prove that the exterior angles so formed are obtuse and equal.

Answer

Ans 1 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 2

In the given figure, AB = AC. Prove that:

(i) DP = DQ

(ii) AP = AQ

(iii) AD bisects angle A

Answer

Ans 2 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 3

In triangle ABC, AB = AC; BE……………… Prove that:

(i) BE = CF

(ii) AF = AE

Answer

Ans 3 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 4

In isosceles triangle ABC, AB = AC. The side BA is produced to D such that BA = AD. Prove that: ∠BCD = 90o

Answer

Ans 4 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 5

(i) In triangle ABC, AB = AC and = 36°. If the internal bisector of ∠C meets AB at point D, prove that AD = BC.

(ii) If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

Answer

Ans 5 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 6

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Answer

Ans 6 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 7

In the given figure, AB = AC and ∠DBC = ∠ECB = 90o

Prove that:

(i) BD = CE

(ii) AD = AE

Answer

Ans 7 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 8

ABC and DBC are two isosceles triangles on the same side of BC. Prove that:

(i) DA (or AD) produced bisects BC at right angle.

(ii) ∠BDA = ∠CDA.

Answer

Ans 8 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 9

The bisectors of the equal angles B and C of an isosceles triangle ABC meet at O. Prove that AO bisects angle A.

Answer

Ans 9 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 10

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

Answer

Ans 10 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 11

Use the given figure to prove that, AB = AC.

Answer

Ans 11 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 12

In the given figure; AE bisects exterior angle CAD and AE is parallel to BC.

Prove that: AB = AC.

Answer

Ans 12 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 13

In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP = BQ = CR. Prove that triangle PQR is equilateral.

Answer

Ans 13 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 14

In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.

Answer

Ans 14 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 15

Through any point in the bisector of angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.

Answer

Ans 15 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 16

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively. Prove that:

(i) PR = QR(ii) BQ = CP

Answer

Ans 16 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

 Question 17

From the following figure, prove that:

(i) ∠ACD = ∠CBE

(ii) AD = CE

Answer

Ans 17 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 18

Equal sides AB and AC of an isosceles triangle ABC are produced. The bisectors of the exterior angle so formed meet at D. Prove that AD bisects angle A.

Answer

Ans 18 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Ans 18 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 19

ABC is a triangle. The bisector of the angle BCA meets AB in X. A point Y lies on CX such that AX = AY.

Prove that ∠CAY = ∠ABC.

Answer

Ans 19 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 20

In the following figure; IA and IB are bisectors of angles CAB and CBA respectively. CP is parallel to IA and CQ is parallel to IB.

Prove that:

PQ = The perimeter of the ∇ABC.

Answer

Ans 20 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 21

Sides AB and AC of a triangle ABC are equal. BC is produced through C upto a point D such that AC = CD. D and A are joined and produced upto point E. If angle BAE = 108o; find angle ADB.

Answer

Ans 21 Exercise - 10 B Isosceles Triangles ICSE Class-9th Concise Selina Maths Solutions

Question 22

The given figure shows an equilateral triangle ABC with each side 15 cm. Also, DE//BC, DF//AC and EG//AB.

If DE + DF + EG = 20 cm, find FG.

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