Triangles ML Aggarwal ICSE 9th Maths Solutions

Triangles ML Aggarwal ICSE 9th Maths Solutions APC.Step by Step Answer of Exercise-10.1, Exercise-10.2, Exercise-10.3, Exercise-10.4 MCQ and Chapter-Test Questions of  Triangles for ICSE Class-9 Mathematics. So This post is the Answer of  ML Aggarwal Triangles Exercise Questions for ICSE Maths Class-9. Visit official website CISCE for detail information about ICSE Board Class-9th.

Triangles ML Aggarwal ICSE 9th Maths Solutions Chapter-10


–: Select Topics :–

 Exercise-10.1Exercise-10.2,

 Exercise-10.3,  Exercise-10.3, 

 MCQ   Chapter-Test , 

Note:- Before viewing Solution of triangle Chapter of ML Aggarwal ICSE Class-9 Maths clear the next point. Angle sum property and concurrency of triangle is the base of this chapter but inequality in Triangle  is also important properties in this chapter.Type of triangle on the base of angle and on the base of side should be clear before solving this chapter . Incentre and Incircle topic with circumcentre and circumcircle  are main concept of Triangle.


Exercise 10.1 Triangles ML Aggarwal Solutions 

Question 1.

It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR ? Why?

Answer 1

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1

Question 2.

“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Answer 2

No, it is not true statement as the angles should be included angle of there two given sides.

Question 3.

In the given figure, AB=AC and AP=AQ. Prove that
(i) ∆APC ≅ ∆AQB
(ii) CP = BQ
(iii) ∠APC = ∠AQB.

Answer 3

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 3a

Question 4.

In the given figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that
(i) ∆APC ≅ ∆AQB
(ii) CP = BQ
(iii) ∠ACP = ∠ABQ.

Answer 4

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 4a

Question 5.

In the given figure, AD = BC and BD = AC. Prove that :
∠ADB = ∠BCA and ∠DAB = ∠CBA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 5

Answer 5 
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 5q

Question 6.

In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that
(i) ∆ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.

Answer 6

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 6

Question 7.

In the given figure, AB = DC and AB || DC. Prove that AD = BC.

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 7
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 7a

Question 8

In the given figure. AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 8

Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 8a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 8b

Question 9.

In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that
(i) ∆ACE ≅ ∆DBF
(ii) AE = DF.

Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 9

Question 10.

In the given figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that
(i) ∆ABD ≅ ∆ACD
(ii) AD is bisector of ∠A
(iii) AD is perpendicular to BC.

Answer 10

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 10
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 10a

Question 11.

Two line segments AB and CD bisect each other at O. Prove that :
(i) AC = BD
(ii) ∠CAB = ∠ABD
(iii) AD || CB
(iv) AD = CB.

Answer 11

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 11
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 11a

Question 12.

In each of the following diagrams, find the values of x and y.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 12
Answer 12

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex1 12a


 Triangle Answer of Exercise 10.2 for Class-9 Understanding

Question 1.

In triangles ABC and PQR, ∠A= ∠Q and ∠B = ∠R. Which side of APQR should be equal to side AB of AABC so that the two triangles are congruent? Give reason for your answer.

Answer 1

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 1a

Question 2.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of APQR should be equal to side BC of AABC so that the two triangles are congruent? Give reason for your answer.

Answer 2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 2

Question 3.

“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent”. Is the statement true? Why?

Answer 3

The given statement can be true only if the corresponding (included) sides are equal otherwise not.

Question 4.

In the given figure, AD is median of ∆ABC, BM and CN are perpendiculars drawn from B and C respectively on AD and AD produced. Prove that BM = CN.

Answer 4

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 4a

Question 5.

In the given figure, BM and DN are perpendiculars to the line segment AC. If BM = DN, prove that AC bisects BD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 5

Answer 5

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 5a

Question 6.

In the given figure, l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ∆ABC ≅ ∆CDA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 6

Answer 6

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 6a

Question 7.

In the given figure, two lines AB and CD intersect each other at the point O such that BC || DA and BC = DA. Show that O is the mid-point of both the line segments AB and CD.

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 7
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 7a

Question 8.

In the given figure, ∠BCD = ∠ADC and ∠BCA = ∠ADB. Show that
(i) ∆ACD ≅ ∆BDC
(ii) BC = AD
(iii) ∠A = ∠B.

Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 8

Question 9.

In the given figure, ∠ABC = ∠ACB, D and E are points on the sides AC and AB respectively such that BE = CD. Prove that
(i) ∆EBC ≅ ∆DCB
(ii) ∆OEB ≅ ∆ODC
(iii) OB = OC.

Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 9
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 9a

Question 10.

ABC is an isosceles triangle with AB=AC. Draw AP ⊥ BC to show that ∠B = ∠C.

Answer 10

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 10
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 10a

Question 11.

In the given figure, BA ⊥ AC, DE⊥ DF such that BA = DE and BF = EC.

Answer 11

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 11

Question 12.

ABCD is a rectanige. X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.

Answer 12

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 12

Question 13.

(a) In the figure (1) given below, QX, RX are bisectors of angles PQR and PRQ respectively of A PQR. If XS⊥ QR and XT ⊥ PQ, prove that
(i) ∆XTQ ≅ ∆XSQ
(ii) PX bisects the angle P.
(b) In the figure (2) given below, AB || DC and ∠C = ∠D. Prove that
(i) AD = BC
(ii) AC = BD.
(c) In the figure (3) given below, BA || DF and CA II EG and BD = EC . Prove that, .
(i) BG = DF
(ii) EG = CF.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13a

Answer 13

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13d
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 13e

Question 14.

In each of the following diagrams, find the values of x and y.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 14
Answer 14

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 14a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 14b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 14c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex2 14d


Exercise-10.3 ML Aggarwal Class-9

Question 1.

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Answer 1

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 1

Question 2.

Show that the angles of an equilateral triangle are 60° each.

Answer 2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 2

Question 3.

Show that every equiangular triangle is equilateral.

Answer 3

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 3a

Question 4.

In the following diagrams, find the value of x:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 4
Answer 4

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 4a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 4b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 4c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 4d

Question 5.

In the following diagrams, find the value of x:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5
Answer 5

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5d
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5e
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 5f

Question 6.

(a) In the figure (1) given below, AB = AD, BC = DC. Find ∠ ABC.
(b)In the figure (2) given below, BC = CD. Find ∠ACB.
(c) In the figure (3) given below, AB || CD and CA = CE. If ∠ACE = 74° and ∠BAE =15°, find the values of x and y.

Answer 6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6d
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6e
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 6f

Question 7.

In ∆ABC, AB = AC, ∠A = (5x + 20)° and each of the base angle is \frac { 2 }{ 5 } th of ∠A. Find the measure of ∠A.

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 7

Question 8.

(a) In the figure (1) given below, ABC is an equilateral triangle. Base BC is produced to E, such that BC’= CE. Calculate ∠ACE and ∠AEC.

(b) In the figure (2) given below, prove that ∠ BAD : ∠ ADB = 3 : 1.
(c) In the figure (3) given below, AB || CD. Find the values of x, y and ∠.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 8
Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 8a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 8b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 8c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 8d

Question 9.

In the given figure, D is mid-point of BC, DE and DF are perpendiculars to AB and AC respectively such that DE = DF. Prove that ABC is an isosceles triangle.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 9

Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 9a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 9b

Question 10.

In the given figure, AD, BE and CF arc altitudes of ∆ABC. If AD = BE = CF, prove that ABC is an equilateral triangle.

Answer 10

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 10
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 10a

Question 11.

In a triangle ABC, AB = AC, D and E are points on the sides AB and AC respectively such that BD = CE. Show that:
(i) ∆DBC ≅ ∆ECB
(ii) ∠DCB = ∠EBC
(iii) OB = OC,where O is the point of intersection of BE and CD.

Answer 11

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 11
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 11a

Question 12.

ABC is an isosceles triangle in which AB = AC. P is any point in the interior of ∆ABC such that ∠ABP = ∠ACP. Prove that
(a) BP = CP
(b) AP bisects ∠BAC.

Answer 12

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 12

Question 13.

In the adjoining figure, D and E are points on the side BC of ∆ABC such that BD = EC and AD = AE. Show that ∆ABD ≅ ∆ACE.

Answer 13

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 13
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 13a

Question 14.

(a) In the figure (i) given below, CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ∆ADE ≅ ∆BCE and hence, AEB is an isosceles triangle.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 14
(b) In the figure (ii) given below, O is a point in the interior of a square ABCD such that OAB is an equilateral trianlge. Show that OCD is an isosceles triangle.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 14a

Answer 14

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 14b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 14c

Question 15.

In the given figure, ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2AD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 15

Answer 15

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 15a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex3 15a


Triangle Exercise-10.4 Answer of ML Aggarwal ICSE Class-9

Question 1.

In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is longest? Give reason for your answer.

Answer 1

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 1a

Question 2.

Show that in a right angled triangle, the hypotenuse is the longest side.

Answer 2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 2

Question 3.

PQR is a right angle triangle at Q and PQ : QR = 3:2. Which is the least angle.

Answer 3

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 3a

Question 4.

In ∆ ABC, AB = 8 cm, BC = 5.6 cm and CA = 6.5 cm. Which is (i) the greatest angle ?
(ii) the smallest angle ?

Answer 4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 4

Question 5.

In ∆ABC, ∠A = 50°, ∠B= 60°, Arrange the sides of the triangle in ascending order

.Answer 5

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 5a

Question 6.

In figure given alongside, ∠B = 30°, ∠C = 40° and the bisector of ∠A meets BC at D. Show
(i) BD > AD
(ii) DC > AD
(iii) AC > DC
(iv) AB > BD
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 6

Answer 6

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 6q

Question 7.

(a) In the figure (1) given below, AD bisects ∠A. Arrange AB, BD and DC in the descending order of their lengths.
(b) In the figure (2) given below, ∠ ABD = 65°, ∠DAC = 22° and AD = BD. Calculate ∠ ACD and state (giving reasons) which is greater : BD or DC ?
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 7

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 7a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 7b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 7c

Question 8.

(a) In the figure (1) given below, prove that (i) CF> AF (ii) DC>DF.
(b) In the figure (2) given below, AB = AC.
Prove that AB > CD.
(c) In the figure (3) given below, AC = CD. Prove that BC < CD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8a

Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8d
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8e
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8f
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8g
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 8h

Question 9.

(a) In the figure (i) given below, ∠B < ∠A and ∠C < ∠D. Show that AD < BC. (b) In the figure (ii) given below, D is any point on the side BC of ∆ABC. If AB > AC, show that AB > AD.

Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 9
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 9a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles ex4 9b

Question 10.

(i) Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer,
(ii) Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
(iii) Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.

Answer 10

(i) Length of sides of a triangle are 4 cm, 3 cm and 7 cm
We know that sum of any two sides of a triangle is greatar than its third side But 4 + 3 = 7 cm
Which is not possible
Hence to construction of a triangle with sides 4 cm, 3 cm and 7 cm is not possible.
(ii) Length of sides of a triangle are 9 cm, 7 cm and 17 cm
We know that sum of any two sides of a triangle is greater than its third side Now 9 + 7 = 16 < 17 ∴ It is not possible to construct a triangle with these sides.
(iii) Length of sides of a triangle are 8 cm, 7 cm and 4 cm We know that sum of any two sides of a triangle is greater than its third side Now 7 + 4 = 11 > 8
Yes, It is possible to construct a triangle with these sides.


MCQ Triangle Answer Exercise 10 ML Aggarwal

Choose the correct answer from the given four options (1 to 18):

Question 1.

Which of the following is not a criterion for congruency of triangles?
(a) SAS
(b) ASA
(c) SSA
(d) SSS

Answer 1

Criteria of congruency of two triangles ‘SSA’ is not the criterion. (c)

Question 2.

In the adjoining figure, AB = FC, EF=BD and ∠AFE = ∠CBD. Then the rule by which ∆AFE = ∆CBD is
(a) SAS
(b) ASA
(c) SSS
(d) AAS
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 2
Answer 2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 2a

Question 3.

In the adjoining figure, AB ⊥ BE and FE ⊥ BE. If AB = FE and BC = DE, then
(a) ∆ABD ≅ ∆EFC
(b) ∆ABD ≅ ∆FEC
(c) ∆ABD ≅ ∆ECF
(d) ∆ABD ≅ ∆CEF

Answer 3

In the figure given,
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 3

Question 4.

Answer 4

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 4

Question 5.

In the adjoining figure, O is mid point of AB. If ∠ACO = ∠BDO, then ∠OAC is equal to
(a) ∠OCA
(b) ∠ODB
(c) ∠OBD
(d) ∠BOD

Answer 5

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 5a

Question 6.

In the adjoining figure, AC = BD. If ∠CAB = ∠DBA, then ∠ACB is equal to
(a) ∠BAD
(b) ∠ABC
(c) ∠ABD
(d) ∠BDA
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 6
Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 6a

Question 7.

In the adjoining figure, ABCD is a quadrilateral in which BN and DM are drawn perpendiculars to AC such that BN = DM. If OB = 4 cm, then BD is
(a) 6 cm
(b) 8 cm
(c) 10 cm
(d) 12 cm

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 7
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 7a

Question 8.

In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to
(a) 40°
(b) 50°
(c) 80°
(d) 130°

Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 8

Question 9.

In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to
(a) 80°
(b) 40°
(c) 50°
(d) 100°

Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 9
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 9a

Question 10.

In ∆PQR, ∠R = ∠P, QR = 4 cm and PR = 5 cm. Then the length of PQ is
(a) 4 cm
(b) 5 cm
(c) 2 cm
(d) 2.5 cm

Answer 10

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 10

Question 11.

In ∆ABC and APQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but isosceles
(d) neither congruent nor isosceles

Answer 11

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 11
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 11a

Question 12.

Two sides of a triangle are of lenghts 5 cm and 1.5 cm. The length of the third side of the triangle can not be
(a) 3.6 cm
(b) 4.1 cm
(c) 3.8 cm
(d) 3.4 cm

Answer 12

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 12

Question 13.

If a, b, c are the lengths of the sides of a trianlge, then
(a) a – b > c
(b) c > a + b
(c) c = a + b
(d) c < A + B

Answer 13

a, b, c are the lengths of the sides of a trianlge than a + b> c or c < a + b
(Sum of any two sides is greater than its third side) (d)

Question 14.

It is not possible to construct a triangle when the lengths of its sides are
(a) 6 cm, 7 cm, 8 cm
(b) 4 cm, 6 cm, 6 cm
(c) 5.3 cm, 2.2 cm, 3.1 cm
(d) 9.3 cm, 5.2 cm, 7.4 cm

Answer 14

We know that sum of any two sides of a triangle is greater than its third side 2.2 + 3.1 = 5.3 ⇒ 5.3 = 5.3 is not possible (c)

Question 15.

In ∆PQR, if ∠R> ∠Q, then
(a) QR > PR
(b) PQ > PR
(c) PQ < PR
(d) QR < PR

Answer 15

In ∆PQR, ∠R> ∠Q
∴ PQ > PR (b)

Question 16.

If triangle PQR is right angled at Q, then
(a) PR = PQ
(b) PR < PQ
(c) PR < QR
(d) PR > PQ

Answer 16

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 16

Question 17.

If triangle ABC is obtuse angled and ∠C is obtuse, then
(a) AB > BC
(b) AB = BC
(c) AB < BC
(d) AC > AB

Answer 17

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles mcq 17

 

Question 18.

If the lengths of two sides of an isosceles are 4 cm and 10 cm, then the length of the third side is
(a) 4 cm
(b) 10 cm
(c) 7 cm
(d) 14 cm

Answer 18

Lengths of two sides of an isosceles triangle are 4 cm and 10 cm, then length of the third side is 10 cm
(Sum of any two sides of a triangle is greater than its third side and 4 cm is not possible as 4 + 4 > 10 cm.


 Chapter-Test of Triangle Class-9 for ML Aggarwal Answer

Question 1.

In triangles ABC and DEF, ∠A = ∠D, ∠B = ∠E and AB = EF. Will the two triangles be congruent? Give reasons for your answer.

Answer 1

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 1a

Question 2.

In the adjoining  figure, ABCD is a square. P, Q and R are points on the sides AB, BC and CD respectively such that AP= BQ = CR and ∠PQR = 90°. Prove that
(a) ∆PBQ ≅ ∆QCR
(b) PQ = QR
(c) ∠PRQ = 45°
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 2

Answer 2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 2a

 

Question 3.

In the given figure, OA ⊥ OD, OC X OB, OD = OA and OB = OC. Prove that AB = CD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 4
Answer 3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 4a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 4b

 

 

 

 

 

 

 

Question 4.

In the given figure, PQ || BA and RS CA. If BP = RC, prove that:
(i) ∆BSR ≅ ∆PQC
(ii) BS = PQ
(iii) RS = CQ.

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 5

Answer 4

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 5a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 5b

Question 5.

In the given figure, AB = AC, D is a point in the interior of ∆ABC such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ∆ABC.

Answer 5

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 6a

Question 6

In the adjoining figure, AB || DC. CE and DE bisects ∠BCD and ∠ADC respectively. Prove that AB = AD + BC.

Answer 6

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 7

Question 7

In ∆ABC, D is a point on BC such that AD is the bisector of ∠BAC. CE is drawn parallel to DA to meet BD produced at E. Prove that ∆CAE is isosceles

Answer 7

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 8
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 8a

Question 8.

In the figure (ii) given below, ABC is a right angled triangle at B, ADEC and BCFG are squares. Prove that AF = BE.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 9
Answer 8

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 9a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 9b

Question 9

In the given figure, BD = AD = AC. If ∠ABD = 36°, find the value of x .
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 10
Answer 9

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 10a

Question 10

In the adjoining figure, TR = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that RB = SA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 11

Answer 10

Given: In the figure , RST is a triangle
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 11a

Question 11

(a) In the figure (1) given below, find the value of x.
(b) In the figure (2) given below, AB = AC and DE || BC. Calculate
(i)x
(ii) y
(iii) ∠BAC
(c) In the figure (1) given below, calculate the size of each lettered angle.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12

Answer 11

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12d
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12e
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 12f

Question 12

(a) In the figure (1) given below, AD = BD = DC and ∠ACD = 35°. Show that
(i) AC > DC (ii) AB > AD.
(b) In the figure (2) given below, prove that
(i) x + y = 90° (ii) z = 90° (iii) AB = BC
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 13

Answer 12

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 13a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 13b
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 13c
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 13d

Question 13.

In the adjoining  figure, ABC and DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP ≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D
(iv) AP is the perpendicular bisector of BC.

Answer 13

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 14
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 14a

Question 14

In the given figure, AP ⊥ l and PR > PQ. Show that AR > AQ.

Answer 14

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 15

Question 15

If O is any point in the interior of a triangle ABC, show that
OA + OB + OC > \frac { 1 }{ 2 }
(AB + BC + CA).
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 16
Answer 15

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 16a
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 10 Triangles Chapter Test 16b

Return to ML Aggarawal Maths Solutions for ICSE  Class-9.


Thanks

 

Share with your friends

 

error: Content is protected !!