Class 9 RD SHARMA Solutions Maths Chapter 12 - Congruent Triangles
Ex. 12.1
Ex. 12.2
Ex. 12.3
Ex. 12.4
Ex. 12.5
Ex. 12.6
12.85
12.86
12.87
12.88
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
Congruent Triangles Exercise Ex. 12.2
Solution 1
Solution 2
Solution 3
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
Congruent Triangles Exercise Ex. 12.4
Solution 1
Solution 2
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
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
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
Congruent Triangles Exercise 12.86
Solution 11
Solution 12
Solution 13
Solution 14
Congruent Triangles Exercise 12.87
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Congruent Triangles Exercise 12.88
Solution 20