Isosceles Triangles Concise Class-9th Selina ICSE Maths

By PANDEY TUTORIAL On Jun 4, 2020

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.

–: Select Topics :–

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 = 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.