# NCERT Solutions for Class 9 Maths Exercise 7.2

## myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

NCERT solutions for Class 9 Maths Triangles

## NCERT Solutions for Class 9 Mathematics Triangles

###### 1. In an isosceles triangle ABC, with AB = AC, the bisectors of B and C intersect each other at O. Join A to O. Show that:

(i) OB = OC

(ii) AO bisects A.

Ans. (i) ABC is an isosceles triangle in which AB = AC.

C = B [Angles opposite to equal sides]

OCA + OCB = OBA + OBC

OB bisects B and OC bisects C

OBA = OBC and OCA = OCB

OCB + OCB = OBC + OBC

2OCB = 2OBC

OCB = OBC

Now in OBC,

OCB = OBC [Prove above]

OB = OC [Sides opposite to equal sides]

(ii) In AOB and AOC,

AB = AC [Given]

OBA = OCA [Given]

And B = C

B = C

OBA = OCA

OB = OC [Prove above]

AOB AOC [By SAS congruency]

OAB = OAC [By C.P.C.T.]

Hence AO bisects A.

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 2. In ABC, AD is the perpendicular bisector of BC (See figure). Show that ABC is an isosceles triangle in which AB = AC.

Ans. In AOB and AOC,

BD = CD [AD bisects BC]

ABD ACD [By SAS congruency]

AB = AC [By C.P.C.T.]

Therefore, ABC is an isosceles triangle.

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 3. ABC is an isosceles triangle in which altitudes BE and CF are drawn to sides AC and AB respectively (See figure). Show that these altitudes are equal.

Ans. In ABE and ACF,

A= A [Common]

AEB = AFC = [Given]

AB = AC [Given]

ABE ACF [By ASA congruency]

BE = CF [By C.P.C.T.]

Altitudes are equal.

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (See figure). Show that:

(i) ABE ACF

(ii) AB = AC or ABC is an isosceles triangle.

Ans. (i) In ABE and ACF,

A= A [Common]

AEB = AFC = [Given]

BE = CF [Given]

ABE ACF [By ASA congruency]

(ii) Since ABE ACF

BE = CF [By C.P.C.T.]

ABC is an isosceles triangle.

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 5. ABC and DBC are two isosceles triangles on the same base BC (See figure). Show that ABD = ACD.

Ans. In isosceles triangle ABC,

AB = AC [Given]

ACB = ABC …….(i) [Angles opposite to equal sides]

Also in Isosceles triangle BCD.

BD = DC

BCD = CBD ……….(ii) [Angles opposite to equal sides]

ACB + BCD = ABC + CBD

ACD = ABD

Or ABD = ACD

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 6. ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that BCD is a right angle (See figure).

Ans. In isosceles triangle ABC,

AB = AC [Given]

ACB = ABC …….(i) [Angles opposite to equal sides]

Now AD = AB [By construction]

But AB = AC [Given]

ADC = ACD ………(ii) [Angles opposite to equal sides]

Since BAC + CAD = ………(iii) [Linear pair]

###### And Exterior angle of a triangle is equal to the sum of its interior opposite angles.

In ABC,

CAD = ABC + ACB = ACB + ACB [Using (i)]

= ACD + ACD = 2 ACD ……….(v)

From eq. (iii), (iv) and (v),

2ACB + 2ACD =

2(ACB + ACD) =

ACB + ACD =

BCD =

Hence BCD is a right angle.

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 7. ABC is a right angled triangle in which A = and AB = AC. Find B and C.

Ans. ABC is a right triangle in which,

A = And AB = AC

In ABC,

AB = AC

C = B ……….(i)

We know that, in ABC,

A + B + C = [Angle sum property]

B + B =

[A = (given) and B = C (from eq. (i)]

2B =

B =

Also C = [B = C]

NCERT Solutions for Class 9 Maths Exercise 7.2

###### 8. Show that the angles of an equilateral triangle are each.

Ans. Let ABC be an equilateral triangle.

AB = BC = AC

AB = BC

C = A ……….(i)

Similarly, AB = AC

C = B ……….(ii)

From eq. (i) and (ii),

A = B = C ……….(iii)

Now in ABC

A + B + C = ……….(iv)

A + A + A =

3A =

A =

Since A = B = C [From eq. (iii)]

A = B = C =

Hence each angle of equilateral triangle is

## NCERT Solutions for Class 9 Maths Exercise 7.2

NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

## CBSE app for Class 9

To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question papers online with solution using our databank of 5,00,000+ questions and download as PDF with your own name & logo in minutes.

### 6 thoughts on “NCERT Solutions for Class 9 Maths Exercise 7.2”

1. very nice solutions.

2. very nice solutions

3. Very good solutions, thanks.

4. All Ouestion solution or best

5. That was really osm…..when my maths teacher explained it…I didn’t understand….but now the topic is very clear…..thanku so much……

6. These answers are correct. But I don’t need any help because I am the most knowledgeable ?.

??I m joking this really help me