NCERT Solution - Triangles Class 9 Notes | EduRev

Created by: Zinga

Class 9 : NCERT Solution - Triangles Class 9 Notes | EduRev

 Page 1


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 7 – Triangles   
Maths   
   
  
Exercise 7.1 Question  
1:   
In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that 
?ABC  ?ABD. What can you say about BC and BD?   
   
Answer:   
In ?ABC and ?ABD,   
AC = AD (Given)   
CAB = DAB (AB bisects  A)   
AB = AB (Common)   
 ?ABC  ?ABD (By SAS congruence rule)   
 BC = BD (By CPCT)   
Therefore, BC and BD are of equal lengths.   
Question 2:   
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (See the given figure).   
Page 2


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 7 – Triangles   
Maths   
   
  
Exercise 7.1 Question  
1:   
In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that 
?ABC  ?ABD. What can you say about BC and BD?   
   
Answer:   
In ?ABC and ?ABD,   
AC = AD (Given)   
CAB = DAB (AB bisects  A)   
AB = AB (Common)   
 ?ABC  ?ABD (By SAS congruence rule)   
 BC = BD (By CPCT)   
Therefore, BC and BD are of equal lengths.   
Question 2:   
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (See the given figure).   
Cbse-spot.blogspot.com  
2 
  
Prove that    
(i) ?ABD  ?BAC   
(ii) BD = AC   
 
(iii) ABD = 
 
BAC.   
   
Answer:   
In ?ABD and ?BAC,   
AD = BC (Given)   
  
DAB = CBA (Given)   
AB = BA (Common)   
 ?ABD  ?BAC (By SAS congruence rule)   
 BD = AC (By CPCT) And,  ABD  
=  BAC (By CPCT)   
Question 3:   
AD and BC are equal perpendiculars to a line segment AB (See the given figure).   
Show that CD bisects AB.   
Page 3


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 7 – Triangles   
Maths   
   
  
Exercise 7.1 Question  
1:   
In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that 
?ABC  ?ABD. What can you say about BC and BD?   
   
Answer:   
In ?ABC and ?ABD,   
AC = AD (Given)   
CAB = DAB (AB bisects  A)   
AB = AB (Common)   
 ?ABC  ?ABD (By SAS congruence rule)   
 BC = BD (By CPCT)   
Therefore, BC and BD are of equal lengths.   
Question 2:   
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (See the given figure).   
Cbse-spot.blogspot.com  
2 
  
Prove that    
(i) ?ABD  ?BAC   
(ii) BD = AC   
 
(iii) ABD = 
 
BAC.   
   
Answer:   
In ?ABD and ?BAC,   
AD = BC (Given)   
  
DAB = CBA (Given)   
AB = BA (Common)   
 ?ABD  ?BAC (By SAS congruence rule)   
 BD = AC (By CPCT) And,  ABD  
=  BAC (By CPCT)   
Question 3:   
AD and BC are equal perpendiculars to a line segment AB (See the given figure).   
Show that CD bisects AB.   
Cbse-spot.blogspot.com  
3 
  
   
Answer:   
In ?BOC and ?AOD,   
BOC =  AOD (Vertically opposite angles)   
CBO =  DAO (Each 90º)   
BC = AD (Given)   
 ?BOC  ?AOD (AAS congruence rule)   
 BO = AO (By CPCT)   
 CD bisects AB.   
Question 4:  l and m are two parallel lines intersected by another pair of parallel lines 
p and q (see  
 
the given figure). Show that ?ABC  ?CDA.   
   
Answer:   
In ?ABC and ?CDA,   
Page 4


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 7 – Triangles   
Maths   
   
  
Exercise 7.1 Question  
1:   
In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that 
?ABC  ?ABD. What can you say about BC and BD?   
   
Answer:   
In ?ABC and ?ABD,   
AC = AD (Given)   
CAB = DAB (AB bisects  A)   
AB = AB (Common)   
 ?ABC  ?ABD (By SAS congruence rule)   
 BC = BD (By CPCT)   
Therefore, BC and BD are of equal lengths.   
Question 2:   
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (See the given figure).   
Cbse-spot.blogspot.com  
2 
  
Prove that    
(i) ?ABD  ?BAC   
(ii) BD = AC   
 
(iii) ABD = 
 
BAC.   
   
Answer:   
In ?ABD and ?BAC,   
AD = BC (Given)   
  
DAB = CBA (Given)   
AB = BA (Common)   
 ?ABD  ?BAC (By SAS congruence rule)   
 BD = AC (By CPCT) And,  ABD  
=  BAC (By CPCT)   
Question 3:   
AD and BC are equal perpendiculars to a line segment AB (See the given figure).   
Show that CD bisects AB.   
Cbse-spot.blogspot.com  
3 
  
   
Answer:   
In ?BOC and ?AOD,   
BOC =  AOD (Vertically opposite angles)   
CBO =  DAO (Each 90º)   
BC = AD (Given)   
 ?BOC  ?AOD (AAS congruence rule)   
 BO = AO (By CPCT)   
 CD bisects AB.   
Question 4:  l and m are two parallel lines intersected by another pair of parallel lines 
p and q (see  
 
the given figure). Show that ?ABC  ?CDA.   
   
Answer:   
In ?ABC and ?CDA,   
Cbse-spot.blogspot.com  
4 
  
BAC = DCA (Alternate interior angles, as p || q)  
AC = CA (Common)   
BCA = DAC (Alternate interior angles, as l || m)   
 ?ABC  ?CDA (By ASA congruence rule)   
Question 5:   
Line l A is the bisector of an angle and B is any point on l. BP and BQ are 
perpendiculars from B to the arms of A (see the given figure). Show that: i) ?APB   
?AQB ( ii) BP = BQ or B is equidistant from the arms of (  A.   
   
Answer:   
In ?APB and ?AQB,   
APB = AQB (Each 90º)   
PAB = QAB (l is the angle bisector of A)   
AB = AB (Common)   
 ?APB  ?AQB (By AAS congruence rule)   
BP = BQ (By CPCT)   
rms of A. Or, 
it can be said that B is equidistant from the a  
Question 6:   
In the given figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE.   
Page 5


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 7 – Triangles   
Maths   
   
  
Exercise 7.1 Question  
1:   
In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that 
?ABC  ?ABD. What can you say about BC and BD?   
   
Answer:   
In ?ABC and ?ABD,   
AC = AD (Given)   
CAB = DAB (AB bisects  A)   
AB = AB (Common)   
 ?ABC  ?ABD (By SAS congruence rule)   
 BC = BD (By CPCT)   
Therefore, BC and BD are of equal lengths.   
Question 2:   
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (See the given figure).   
Cbse-spot.blogspot.com  
2 
  
Prove that    
(i) ?ABD  ?BAC   
(ii) BD = AC   
 
(iii) ABD = 
 
BAC.   
   
Answer:   
In ?ABD and ?BAC,   
AD = BC (Given)   
  
DAB = CBA (Given)   
AB = BA (Common)   
 ?ABD  ?BAC (By SAS congruence rule)   
 BD = AC (By CPCT) And,  ABD  
=  BAC (By CPCT)   
Question 3:   
AD and BC are equal perpendiculars to a line segment AB (See the given figure).   
Show that CD bisects AB.   
Cbse-spot.blogspot.com  
3 
  
   
Answer:   
In ?BOC and ?AOD,   
BOC =  AOD (Vertically opposite angles)   
CBO =  DAO (Each 90º)   
BC = AD (Given)   
 ?BOC  ?AOD (AAS congruence rule)   
 BO = AO (By CPCT)   
 CD bisects AB.   
Question 4:  l and m are two parallel lines intersected by another pair of parallel lines 
p and q (see  
 
the given figure). Show that ?ABC  ?CDA.   
   
Answer:   
In ?ABC and ?CDA,   
Cbse-spot.blogspot.com  
4 
  
BAC = DCA (Alternate interior angles, as p || q)  
AC = CA (Common)   
BCA = DAC (Alternate interior angles, as l || m)   
 ?ABC  ?CDA (By ASA congruence rule)   
Question 5:   
Line l A is the bisector of an angle and B is any point on l. BP and BQ are 
perpendiculars from B to the arms of A (see the given figure). Show that: i) ?APB   
?AQB ( ii) BP = BQ or B is equidistant from the arms of (  A.   
   
Answer:   
In ?APB and ?AQB,   
APB = AQB (Each 90º)   
PAB = QAB (l is the angle bisector of A)   
AB = AB (Common)   
 ?APB  ?AQB (By AAS congruence rule)   
BP = BQ (By CPCT)   
rms of A. Or, 
it can be said that B is equidistant from the a  
Question 6:   
In the given figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE.   
Cbse-spot.blogspot.com  
5 
  
   
Answer:   
It is given that BAD = EAC   
BAD + DAC = EAC + DAC   
BAC = DAE   
In ?BAC and ?DAE,  AB 
= AD (Given)  BAC = 
DAE (Proved above)   
AC = AE (Given)   
 ?BAC  ?DAE (By SAS congruence rule)   
 BC = DE (By CPCT)   
Question 7:   
AB is a line segment and P is its mid-point. D and E are points on the same side of AB  
such that BAD = ABE and EPA = DPB (See the given figure). Show that  i)  
?DAP  ?EBP (   
(ii) AD = BE   
   
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 9

Content Category

Related Searches

NCERT Solution - Triangles Class 9 Notes | EduRev

,

Important questions

,

Semester Notes

,

mock tests for examination

,

Summary

,

Previous Year Questions with Solutions

,

Exam

,

MCQs

,

NCERT Solution - Triangles Class 9 Notes | EduRev

,

pdf

,

Sample Paper

,

Extra Questions

,

NCERT Solution - Triangles Class 9 Notes | EduRev

,

study material

,

practice quizzes

,

Free

,

Objective type Questions

,

ppt

,

past year papers

,

Viva Questions

,

shortcuts and tricks

,

video lectures

;