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

#### Question 1

In the figure alongside,

……………

AB = AC

A = 48^{o} and

Angel ACD = 18^{o}.

Show that BC = CD.

#### Answer

#### Question 2

Calculate:

(i) ∠ADC

(ii) ∠ABC

(iii) ∠BAC

#### Answer

#### Question 3

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

(i) ∠CDE

(ii) ∠ DCE

#### Answer

#### Question 4

Calculate x:

(i)………………….

(ii)…………………….

#### Answer

#### Question 5

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

#### Answer

#### Question 6

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

(i) ∠LMN

(ii) ∠MLN

#### Answer

#### Question 7

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

Find: (i) ∠DCB (ii) ∠CBD.

#### Answer

#### Question 8

Find x:

…………………..

#### Answer

#### 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

#### Question 10

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

#### Answer

#### Question 11

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

Find angle CAB.

#### Answer

#### Question 12

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

#### Answer

#### Question 13

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

#### Answer

#### Question 14

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

#### Answer

#### Question 15

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

#### Answer

#### 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

#### Question 17

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

#### Answer

#### Question 18

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

#### Answer

#### 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

#### Question 20

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

Prove that: BD = BE.

#### Answer

### 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

#### Question 2

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

(i) DP = DQ

(ii) AP = AQ

(iii) AD bisects angle A

#### Answer

#### Question 3

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

(i) BE = CF

(ii) AF = AE

#### Answer

#### Question 4

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

#### Answer

#### 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

#### Question 6

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

#### Answer

#### Question 7

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

Prove that:

(i) BD = CE

(ii) AD = AE

#### Answer

#### 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

#### 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

#### Question 10

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

#### Answer

#### Question 11

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

#### Answer

#### Question 12

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

Prove that: AB = AC.

#### Answer

#### 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

#### Question 14

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

#### Answer

#### 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

#### 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

#### Question 17

From the following figure, prove that:

(i) ∠ACD = ∠CBE

(ii) AD = CE

#### Answer

#### 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

#### 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

#### 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

#### 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 = 108^{o}; find angle ADB.

#### Answer

#### 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.

#### Answer

#### Question 23

If all the three altitudes of a triangle are equal, the triangle is equilateral. Prove it.

#### Answer

#### Question 24

In a ABC, the internal bisector of angle A meets opposite side BC at point D. Through vertex C, line CE is drawn parallel to DA which meets BA produced at point E. Show that ACE is ∇ isosceles.

#### Answer

#### Question 25

In triangle ABC, bisector of angle BAC meets opposite side BC at point D. If BD = CD, prove that ABC is ∇isosceles.

#### Answer

#### Question 26

In ∇ABC, D is point on BC such that AB = AD = BD = DC. Show that:

∠ADC: ∠C = 4: 1.

#### Answer

#### Question 27

Using the information given in each of the following figures, find the values of a and b.

[Given: CE = AC]

#### Answer

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