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.
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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 = 48o and
Angel ACD = 18o.
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 = 110o. Calculate:
(i) ∠LMN
(ii) ∠MLN
Answer
Question 7
An isosceles triangle ABC has AC = BC. CD bisects AB at D and CAB = 55o.
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 = 58o.
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 = 60o, ∠C = 40o, and bisector of angle ABC meets side AC at point P. Show that BP = CP.
Answer
Question 15
In triangle ABC; angle ABC = 90o 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 = 90o
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 = 90o
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 = 108o; 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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