RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and Inequalities in a Triangle


Here you can get solutions of RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and Inequalities in a Triangle. These Solutions are part of RS Aggarwal Solutions Class 9. we have given RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and Inequalities in a Triangle download pdf.





RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and Inequalities in a Triangle





Exercise 5A





Question 1:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q1





Question 2:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q2-1
Consider the isosceles triangle ∆ABC.
Since the vertical angle of ABC is 100° , we have, ∠A = 100°.
By angle sum property of a triangle, we have,
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q2-2





Read More:





Question 3:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q3





Question 4:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q4





Question 5:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q5-1
In a right angled isosceles triangle, the vertex angle is ∠A = 90° and the other two base angles are equal.
Let x° be the base angle and we have, ∠B = ∠C = 90°.
By angle sum property of a triangle, we have
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q5-2





Question 6:
Given: ABC is an isosceles triangle in which AB=AC and BC
Is produced both ways,
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q6





Question 7:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q7-1
Let be an equilateral triangle.
Since it is an equilateral triangle, all the angles are equiangular and the measure of each angle is 60°
The exterior angle of ∠A is ∠BAF
The exterior angle of ∠B is ∠ABD
The exterior angle of ∠C is ∠ACE
We can observe that the angles ∠A and ∠BAF, ∠B and ∠ABD, ∠C and ∠ACE and form linear pairs.
Therefore, we have
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q7-2
Similarly, we have
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q7-3
Also, we have
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q7-4
Thus, we have, ∠BAF = 120°, ∠ABD = 120°, ∠ACE = 120°
So, the measure of each exterior angle of an equilateral triangle is 120°.





Question 8:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q8





Question 9:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q9





Question 10:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q10





Question 11:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q11





Question 12:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q12





Question 13:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q13





Question 14:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q14





Question 15:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q15





Question 16:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q16





Question 17:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q17





Question 18:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q18





Question 19:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q19





Question 20:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q20





Question 21:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q21





Question 22:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q22-1
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q22-2





Question 23:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q23





Question 24:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q24





Question 25:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q25





Question 26:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q26





Question 27:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q27





Question 28:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q28





Question 29:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q29





Question 30:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q30





Question 31:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q31





Question 32:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q32





Question 33:
Let AB be the breadth of a river. Now take a point M on that bank of the river where point B is situated. Through M draw a perpendicular and take point N on it such that point, A, O and N lie on a straight line where point O is the mid point of BM.
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q33





Question 34
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q34





Question 35:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q35





Question 36:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q36





Question 37:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q37





Question 38:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q38





Question 39:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q39





Question 40:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q40





Question 41:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q41





Question 42:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q42





Question 43:
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q43





Question 44:
Given : ABC is a triangle and O is appoint inside it.
rs-aggarwal-class-9-solutions-congruence-of-triangles-and-inequalities-in-a-triangle-5a-q44
To Prove : (i) AB+AC > OB +OC
(ii) AB+BC+CA > OA+OB+OC
(iii) OA+OB+OC > [latex]frac { 1 }{ 2 }  [/latex] (AB+BC+CA)
Proof:
(i) In ∆ABC,
AB+AC > BC ….(i)
And in , ∆OBC,
OB+OC > BC ….(ii)
Subtracting (i) from (i) we get
(AB+AC) – (OB+OC) > (BC-BC)
i.e. AB+AC>OB+OC
(ii) AB+AC > OB+OC [proved in (i)]
Similarly, AB+BC > OA+OC
And AC+BC > OA +OB
Adding both sides of these three inequalities, we get
(AB+AC) + (AC+BC) + (AB+BC) > OB+OC+OA+OB+OA+OC
i.e. 2(AB+BC+AC) > 2(OA+OB+OC)
Therefore, we have
AB+BC+AC > OA+OB+OC
(iii) In ∆OAB
OA+OB > AB ….(i)
In ∆OBC,
OB+OC > BC ….(ii)
And, in ∆OCA,
OC+OA > CA
Adding (i), (ii) and (iii) we get
(OA+OB) + (OB+OC) + (OC+OA) > AB+BC+CA
i.e 2(OA+OB+OC) > AB+BC+CA
⇒ OA+OB+OC > [latex]frac { 1 }{ 2 }  [/latex] (AB+BC+CA)





Question 45:
Since AB=3cm and BC=3.5 cm
∴ AB+BC=(3+3.5) cm =6.5 m
And CA=6.5 cm
So AB+BC=CA
A triangle can be drawn only when the sum of two sides is greater than the third side.
So, with the given lengths a triangle cannot be drawn.





Complete RS Aggarwal Solutions Class 9





If You have any query regarding this chapter, please comment on below section our team will answer you. We Tried our best to give complete solutions so you got good marks in your exam.





If these solutions have helped you, you can also share alarity.in to your friends.





Best of Luck For Your Future!!


RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and Inequalities in a Triangle RS Aggarwal Solutions Class 9 Chapter 5 Congruence of Triangles and
Inequalities in a Triangle Reviewed by Admin on November 15, 2020 Rating: 5

No comments:

Powered by Blogger.