RD SHARMA Solutions for Class 9 Maths Chapter 12 - Congruent Triangles
Chapter 12 - Congruent Triangles Exercise Ex. 12.1
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Chapter 12 - Congruent Triangles Exercise Ex. 12.2
Solution 1
Solution 2
Solution 3
Chapter 12 - Congruent Triangles Exercise Ex. 12.3
Solution 1
Let ABC and DEF be two right triangles.
Solution 2
Solution 3
Solution 4
Let us consider that ABC is an equilateral triangle.
So, AB = BC = AC
Now, AB = AC
So, AB = BC = AC
Now, AB = AC
⇒ ∠C = ∠B (angles opposite to equal sides of a triangle are equal)
We also have
AC = BC
⇒ ∠B = ∠A (angles opposite to equal sides of a triangle are equal)
So, we have
∠A = ∠B = ∠C
Now, in ΔABC
∠A + ∠B + ∠C = 180o
⇒ ∠A + ∠A + ∠A = 180o
⇒ 3∠A = 180o
⇒ ∠A = 60o
⇒ ∠A = ∠B = ∠C = 60o
Hence, in an equilateral triangle all interior angles are of 60o.
We also have
AC = BC
⇒ ∠B = ∠A (angles opposite to equal sides of a triangle are equal)
So, we have
∠A = ∠B = ∠C
Now, in ΔABC
∠A + ∠B + ∠C = 180o
⇒ ∠A + ∠A + ∠A = 180o
⇒ 3∠A = 180o
⇒ ∠A = 60o
⇒ ∠A = ∠B = ∠C = 60o
Hence, in an equilateral triangle all interior angles are of 60o.
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Chapter 12 - Congruent Triangles Exercise Ex. 12.4
Solution 1
Solution 2
Chapter 12 - Congruent Triangles Exercise Ex. 12.5
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
(i) False
(ii) True
(iii) True
(iv) False
(v) True
(vi) False
(vii) False
(viii) False
(ix) True
Solution 6
(i) equal
(ii) equal
(iii) equal
(iv) BC
(v) AC
(vi) equal to
(vii) EFD
Solution 7
Chapter 12 - Congruent Triangles Exercise Ex. 12.6
Solution 1
Solution 2
Solution 3
Solution 4
Here, 2 + 3 < 7
Hence, it is not possible because triangle can be drawn only if the sum of any two sides is greater than third side.
Solution 5
Solution 6
Solution 7
Solution 8
(i) False
(ii) True
(iii) True
(iv) False
(v) True
(vi) True
Solution 9
(i) largest
(ii) less
(iii) greater
(iv) smaller
(v) less
(vi) greater
Solution 10
Solution 11
Chapter 12 - Congruent Triangles Exercise 12.85
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Chapter 12 - Congruent Triangles Exercise 12.86
Solution 11
Solution 12
Solution 13
Solution 14
Chapter 12 - Congruent Triangles Exercise 12.87
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Chapter 12 - Congruent Triangles Exercise 12.88
Solution 20
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