Our ncert solutions for Exercise 7.3 Class 9 maths 7. Triangles - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

# Exercise 7.3 Class 9 maths 7. Triangles - ncert solutions - Toppers Study

Topper Study classes prepares ncert solutions on practical base problems and comes out with the best result that helps the students and teachers as well as tutors and so many ecademic coaching classes that they need in practical life. Our ncert solutions for Exercise 7.3 Class 9 maths 7. Triangles - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

## Exercise 7.3 Class 9 maths 7. Triangles - ncert solutions - Toppers Study

CBSE board students who preparing for **class 9 ncert solutions maths and Mathematics** solved exercise **chapter 7. Triangles** available and this helps in upcoming exams
2023-2024.

### You can Find Mathematics solution Class 9 Chapter 7. Triangles

- All Chapter review quick revision notes for chapter 7. Triangles Class 9
- NCERT Solutions And Textual questions Answers Class 9 Mathematics
- Extra NCERT Book questions Answers Class 9 Mathematics
- Importatnt key points with additional Assignment and questions bank solved.

NCERT Solutions do not only help you to cover your syllabus but also will give to textual support in exams 2023-2024 to complete **exercise 7.3 maths class 9 chapter 7** in english medium. So revise and practice these all cbse study materials like class 9 maths chapter 7.3 in english ncert book. Also ensure to repractice all syllabus within time or before board exams for ncert class 9 maths ex 7.3 in english.

See all solutions for class 9 maths chapter 7 exercise 7 in english medium solved questions with answers.

### Exercise 7.3 class 9 Mathematics Chapter 7. Triangles

Sure! The following topics will be covered in this article

- Exercise 7.3 Class 9 Maths 7. Triangles - Ncert Solutions - Toppers Study
- Class 9 Ncert Solutions
- Solution Chapter 7. Triangles Class 9
- Solutions Class 9
- Chapter 7. Triangles Exercise 7.3 Class 9

## 7. Triangles

### | Exercise 7.3 |

## Exercise 7.3 Class 9 maths 7. Triangles - ncert solutions - Toppers Study

**EXERCISE- 7.3**

**1.Δ ABC and Δ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that:**

**(i) Δ ABD ≅ Δ ACD**

**(ii) Δ ABP ≅ Δ ACP**

**(iii) AP bisects ∠ A as well as ∠ D.**

**(iv) AP is the perpendicular bisector of BC.**

**Solution: **

**Given: **Δ ABC and Δ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC.

**To prove: **

(i) Δ ABD ≅ Δ ACD

(ii) Δ ABP ≅ Δ ACP

(iii) AP bisects ∠ A as well as ∠ D.

(iv) AP is the perpendicular bisector of BC

**Proof:**

In ΔABD and Δ ACD

AB = AC [given]

BD = CD [given]

AD = AD [common]

By SSS Congruence Criterion Rule

Δ ABD ≅ Δ ACD

∠ BAD = ∠CAD [CPCT]

∠ BAP = ∠CAP [CPCT] …

(ii)In ΔABP and Δ ACP

AB = AC [given]

∠ BAP = ∠CAP [proved above]

AP = AP [common]

By SAS Congruence Criterion Rule

Δ ABP ≅ Δ ACP

BP = CP [CPCT] … 2

∠APB = ∠APC [CPCT]

(iii) ∠ BAP = ∠CAP [From eq. 1]

Hence, AP bisects ∠ A.

Now, In Δ BDP and Δ CDP

BD = CD [given]

BP = CP [given]

DP = DP [common]

By SSS Congruence Criterion Rule

Δ BDP ≅ Δ CDP

∠ BDP = ∠CDP [CPCT]

AP bisects ∠ D.

(iv) AP stands on B

∠APB + ∠APC = 180^{0}

∠APB +∠APB = 180^{0}[proved above]

∠APB = 180^{0 }/2

∠APB = 90^{0}

AP is the perpendicular bisector of BC.

**2. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that**

**(i) AD bisects BC (ii) AD bisects ∠ A.**

**Solution:**

**Given: **AD is an altitude of an isosceles triangle ABC in which AB = AC.

**To prove:** (i) AD bisects BC

(ii) AD bisects ∠ A.

** Proof: **In ∆BAD and ∆CAD

∠ ADB = ∠ADC (Each 90º as AD is an altitude)

AB = AC (Given)

AD = AD (Common)

By RHS Congruence Criterion Rule

∆BAD ≅ ∆CAD

BD = CD (By CPCT)

Hence, AD bisects BC.

∠BAD = ∠CAD (By CPCT)

Hence, AD bisects ∠ A

**3. Two sides AB and BC and median AM of one triangle ABC are respectively**

**equal to sides PQ and QR and median PN of Δ PQR (see Fig. 7.40). Show that:**

**(i) Δ ABM ≅ Δ PQN**

**(ii) Δ ABC ≅ Δ PQR**

**Solution:**

**Given: ** Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of Δ PQR.

**To prove:** (i) Δ ABM ≅ Δ PQN

(ii) Δ ABC ≅ Δ PQR

**Proof: **In ∆ABC, AM is the median to BC.

BM = 1/2 BC ... 1

In ∆PQR, PN is the median to QR.

QN = 1/2 QR ... 2

from eq .1 & 2

BM = QN ... 3

Now in ABM and PQN

AB = PQ (Given)

BM = QN [From equation (3)]

AM = PN [given]

By SSS congruence Criterion rule

∆ABM ≅ ∆PQN

∠B =∠Q [CPCT]

Now in∆ ABC and∆ PQR

AB = PQ [given]

∠B = ∠Q [prove above ]

BC = QR [given]

By SAS congruence Criterion rule

∆ ABC ≅ ∆ PQR

**4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence ****rule, prove that the triangle ABC is isosceles.**

**Solution: **

**Given: ** BE and CF are two equal altitudes of a triangle ABC.

**To prove:** ABC is a isosceles.

**Proof: **In ∆BEC and ∆CFB,

BE = CF (Given)

∠BEC = CFB (Each 90°)

BC = CB (Common)

By RHS congruence Criterion rule

∆BEC ≅ ∆CFB

∠BCE = ∠CBF (By CPCT)

AB = AC [Sides opposite to equal angles of a triangle are equal]

Hence, ABC is isosceles.

**5.** **ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that:**

**∠ B = ∠ C.**

**Solution: **

**Given:** ABC is an isosceles triangle with AB = AC.

**To prove:** ∠ B = ∠ C.

**Construction:** Draw AP ⊥ BC to

**Proof : **In ∆APB and ∆APC

∠APB = ∠APC (Each 90º)

AB =AC (Given)

AP = AP (Common)

By RHS Congruence Criterion Rule

∆APB ≅ ∆APC

∠B = ∠C [CPCT]

##### Other Pages of this Chapter: 7. Triangles

### Select Your CBSE Classes

Important Study materials for classes 06, 07, 08,09,10, 11 and 12. Like CBSE Notes, Notes for Science, Notes for maths, Notes for Social Science, Notes for Accountancy, Notes for Economics, Notes for political Science, Noes for History, Notes For Bussiness Study, Physical Educations, Sample Papers, Test Papers, Mock Test Papers, Support Materials and Books.

*Mathematics Class - 11th*

NCERT Maths book for CBSE Students.

books

## Study Materials List:

##### Solutions ⇒ Class 9th ⇒ Mathematics

## Topper's Study

New Books