**NCERT Solutions Class 9 Maths Chapter 7 Triangles** – Here are all the NCERT solutions for Class 9 Maths Chapter 7. This solution contains questions, answers, images, explanations of the complete Chapter 7 titled Triangles of Maths taught in class 9. If you are a student of class 9 who is using NCERT Textbook to study Maths, then you must come across Chapter 7 Triangles. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 9 Maths Chapter 7 Triangles in one place.

## NCERT Solutions Class 9 Maths Chapter 7 Triangles

Here on **AglaSem Schools**, you can access to **NCERT Book Solutions** in free pdf for Maths for Class 9 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 7 Triangles , Maths, Class 9.

Class | 9 |

Subject | Maths |

Book | Mathematics |

Chapter Number | 7 |

Chapter Name |
Triangles |

### NCERT Solutions Class 9 Maths chapter 7 Triangles

Class 9, Maths chapter 7, Triangles solutions are given below in PDF format. You can view them online or download PDF file for future use.

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### NCERT Solutions Class 9 Maths chapter 7 Triangles- Video

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### Download NCERT Solutions Class 9 Maths chapter 7 Triangles In PDF Format

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### Question & Answer

Q.1:In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?

Ans :In ∆ ABC and ∆ ABD, AC = AD (Given) ∠CAB = ∠ DAB (AB bisects ∠A) AB = AB (Common) Therefore, ∆ ABC ≅ ∆ ABD( By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are Of equal lengths.

Q.2:ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig). Prove that (i) ∆ ABD ≅ ∆ BAC (ii) BD = AC (iii) ∠ ABD = ∠ BAC.

Ans :In ∠ABD and ∠BAC, AD = BC (Given) ∠DAB = ∠CBA(Given) AB = BA (Common) \(\begin{array}{l}{\therefore \triangle \mathrm{ABD}=\Delta \mathrm{BAC}(\mathrm{By} \text { SAS congruence rule) }} \\ {\therefore \mathrm{BD}=\mathrm{AC}(\mathrm{By} \mathrm{CPCT})}\end{array}\) And, ∠ABD = ∠BAC (By CPCT)

Q.3:AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB.

Ans :In ∆ BOC and ∆ AOD, \(\begin{array}{l}{\angle \mathrm{BOC}=\angle \mathrm{AOD}(\text { Vertically opposite angles })} \\ {\angle \mathrm{CBO}=\angle \mathrm{DAO}\left(\text { Each } 90^{\circ}\right)}\end{array}\) \(\begin{array}{l}{\mathrm{BC}=\mathrm{AD}(\text { Given })} \\ {\therefore \Delta \mathrm{BOC}=\triangle \mathrm{AOD} \text { (AAS congruence rule) }} \\ {\therefore \mathrm{BO}=\mathrm{AO}(\mathrm{By} \mathrm{CPCT})} \\ {\Rightarrow \mathrm{CD} \text { bisects } \mathrm{AB}}\end{array}\)

Q.4:l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig). Show that ∆ ABC ≅ ∆ CDA.

Ans :In ∆ ABC and ∆ CDA, \(\begin{array}{l}{\angle B A C=\angle D C A(\text { Alternate interior angles, as } p \| q)} \\ {A C=C A(\text { Common })}\end{array}\) \(\begin{array}{l}{\angle B C A=\angle D A C(\text { Alternate interior angles, as } l \| m)} \\ { \triangle A B C = \Delta C D A(B y \text { ASA congruence rule) }}\end{array}\)

Q.5:Line l is the bisector of an angle ∠ A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see Figure). Show that: (i) ∆ APB ≅ ∆ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

Ans :\(\begin{array}{l}{\text { In } \triangle A P B \text { and } \triangle A Q B \text { . }} \\ {\angle A P B=\angle A Q B\left(E a c h 90^{\circ}\right)}\end{array}\) \(\begin{array}{l}{\angle P A B=\angle Q A B(1 \text { is the angle bisector of } \angle A)} \\ {A B=A B(\text { Common })}\end{array}\) \(\begin{array}{l}{\therefore \triangle \mathrm{APB} \cong \triangle \mathrm{AQB}(\mathrm{By} \text { AAS congruence rule) }} \\ {\therefore \mathrm{BP}=\mathrm{BQ}(\mathrm{By} \mathrm{CPCT})}\end{array}\) Or, it can be said that B is equidistant from the arms of ∠ A.

## NCERT / CBSE Book for Class 9 Maths

You can download the NCERT Book for Class 9 Maths in PDF format for free. Otherwise you can also buy it easily online.

- Click here for NCERT Book for Class 9 Maths
- Click here to buy NCERT Book for Class 9 Maths

### All NCERT Solutions Class 9

- NCERT Solutions for Class 9 English
- NCERT Solutions for Class 9 Hindi
- NCERT Solutions for Class 9 Maths
- NCERT Solutions for Class 9 Science
- NCERT Solutions for Class 9 Social Science
- NCERT Solutions for Class 9 Sanskrit

### All NCERT Solutions

You can also check out NCERT Solutions of other classes here. Click on the class number below to go to relevant NCERT Solutions of Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Class 1 | Class 2 | Class 3 |

Class 4 | Class 5 | Class 6 |

Class 7 | Class 8 | Class 9 |

Class 10 | Class 11 | Class 12 |

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