RD SHARMA Solutions for Class 9 Maths Chapter 12 - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise 12.85

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 9

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is

(a) 100°

(b) 120°

(c) 110°

(d) 130°

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 10

Which of the following is not a criterion for congruence of triangles?

(a) SAS

(b) SSA

(c) ASA

(d) SSS

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise 12.86

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise 12.87

Question 1

In the figure, ABC is an isosceles triangle whose side AC is produced to E. Through C, CD is drawn parallel to BA. The value of x is

(a) 52°

(b) 76°

(c) 156°

(d) 104°

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 5

In figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) 8 cm

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise 12.88

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.1

Question 1

In fig., the sides BA and CA have been produced such that BA = AD and CA = AE.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Prove that the medians of an equilateral triangle are equal.

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles



Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 6

The vertical angle of an isosceles triangle is 100o. Find its base angles.

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 7

 In fig., AB = Ac and ACD = 105°, find BAC. 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 10

In fig., AB =AC and DB = DC, find the ratio ABD = ACD. 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 11

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

                                                                                   OR

ABC is a right-angled triangle in which Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent TrianglesA = 90o and AB = AC. Find Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent TrianglesB and Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent TrianglesC.

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

 


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 13

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See fig.). Show that the line PQ is perpendicular bisector of AB.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.2

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

In fig., it is given RT = TS, 1 = 22 and 4 = 23 prove that ΔRBT  ΔSAT.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.3

Question 1

In two right triangles one side and acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Let ABC and DEF be two right triangles.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4
Show that the angles of an equilateral triangle are 60o each.
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles
 
Let us consider that ABC is an equilateral triangle.
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
 3A = 180o
 A = 60o
 A = B = C = 60o
Hence, in an equilateral triangle all interior angles are of 60o.

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.4

Question 1

In fig., it is given that Ab = CD and AD = BC. prove that ΔADC  ΔCBA

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.5

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

In fig., AD ⊥ CD and CB  CD. If AQ = BP an DP = CQ, prove that DAQ = CBP.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 5

Which of the following statements are True (T) and which are False (f):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilaterial triangle is 60o.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscles.

(v) The bisectors of two equal angles of a traingle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triagnle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Solution 5

(i) False

(ii) True

(iii) True

(iv) False

(v) True

(vi) False

(vii) False

(viii) False

(ix) True

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 6

(i) equal

(ii) equal

(iii) equal

(iv) BC

(v) AC

(vi) equal to

(vii) EFD

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Chapter 12 - Congruent Triangles Exercise Ex. 12.6

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 4

Is it possible to draw a triangle with sides of length 2cm, 3cm and 7 cm?

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.

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 7

In fig., prove that:

i. CD + DA + AB + BC > 2AC

ii. CD + DA + AB > BC

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 8

Which of the following statements are true (T) and which are false (F)?

(i) Sum of the three sides of a triangle is less than the sum of its three altitudes.

(ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side.

(iii) Sum of any two sides of a triangle is greater than the third side.

(iv) Difference of any two sides of a triangle is equal to the third side.

(v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.

(vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

Solution 8

(i) False

(ii) True

(iii) True

(iv) False

(v) True

(vi) True

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 9

(i) largest

(ii) less

(iii) greater

(iv) smaller

(v) less

(vi) greater

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Congruent Triangles