RBSE Solutions for Class 7 Maths Chapter 9 Congruence of Triangles Additional Questions

RBSE Solutions for Class 7 Maths Chapter 9 Congruence of Triangles Additional Questions is part of RBSE Solutions for Class 7 Maths. Here we have given Rajasthan Board RBSE Class 7 Maths Chapter 9 Congruence of Triangles Additional Questions.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 7
Subject	Maths
Chapter	Chapter 9
Chapter Name	Congruence of Triangles
Exercise	Additional Questions
Number of Questions	18
Category	RBSE Solutions

Rajasthan Board RBSE Class 7 Maths Chapter 9 Congruence of Triangles Additional Questions

Multiple Choice Questions

Question 1
One of the angle in two congruent angles is 110° then (RBSESolutions.com) the measure of another angle will be:
(A) 70°
(B) 80°
(C) 110°
(D) 100°

Question 2
In figure what will be the value of ∠X where XY = XZ md ∠Y = 50°.

(A) 80°
(B) 40°
(C) 50°
(D) 90°

Question 3
In R.H.S, condition (RBSESolutions.com) of congruency rules :
(A) Two acute angle triangle
(B) Two right angled triangle
(C) Two obtues angle triangle
(D) Two reflex angle triangle

Question 4
General congruency condition is not satisfied in :
(A) R.H.S.
(B) A.S.A.
(C) S.A.S.
(D)A,A.A.

Question 5
Two circles will be (RBSESolutions.com) congruent if:
(A) radii are equal
(B) centre are equal
(C) chords are equal
(D) are concentric circles

Question 6
Corresponding parts of congurent triangles are :
(A) unequal
(B) congruent
(C) 0
(D) 4

Question 7
Such figures which covers (RBSESolutions.com) completely to each other are called :
(A) symmatric
(B) unsymmatric
(C) congruent
(D)none of these

Question 8
The sign of congruency is :
(A) ≡
(B) ≅
(C) ≈
(D) ∆
Answers:
1. (C), 2. (A), 3. (B), 4. (D), 5. (A), 6. (B), 7. (C), 8. (B).

Fill in the blanks :
(i) Those figures which are (RBSESolutions.com) equal in shape and ………….. are congruent to each other.
(ii) If measures of two angles are equal then they are ………… .
(iii) If two figures A and B are congruent then we will write as …………… .
(iv) If two triangles ∆ABC and ∆PQR given congruent then possible pairs of correspondence are ……… .
Solution:
(i) measure (size)
(ii) congruent
(iii) A ≅ B,
(iv) 6

True/False
(i) ₹50 – 50 notes are same size and shape, it is (RBSESolutions.com) an example of congruency.
(ii) Figures may be different in size in congruency.
(iii) It is not compulsory in R.H.S. condition that one angle is right angle.
(iv) If two sides and including angle of a triangle are equal to the corresponding two sides and angle including by these the triangle will be congruent.
Answer:
(i) T
(ii) F
(iii) F
(iv) T

Very Short Answer Type Questions

Question 1
Give three examples of (RBSESolutions.com) congruent shapes from your real life.
Solution:
(i) Duplicate key of a lock.
(ii) ₹500 – 500 note
(iii) Ployergcards

Question 2
If ∆ABC ≅ ∆FED under the proper pairs of ABC ↔ FED. Then write all the corresponding congruent parts.
Solution:
∆ABC ≅ ∆FED means that ∆ABC covers (RBSESolutions.com) completely and vertices of ∆ABC will be on he vertices of ∆FED.
∴ A ↔ F, B ↔ E and C ↔ D
Corresponding sides will be congruent.
\(\overline { AB }\) ↔ \(\overline { FE }\) , \(\overline { BC }\) ↔ \(\overline { ED }\)and \(\overline { CA }\) ↔ \(\overline { DF }\)
Corresponding angles will be congruent.
∠A ↔ ∠F, ∠B ↔ ∠Eand ∠C ↔ ∠D

Question 3
If ∆DEF ≅ ∆BCA then write the (RBSESolutions.com) name of those parts which are congruent of the following:
(i) ∠E
(ii) \(\overline { EF }\)
(iii)∠F
(iv) \(\overline { DF }\)
Solution:
If ∆DEF = ∆BCA
Then D ↔ B, E ↔ C and F ↔ A
∴ Corresponding (RBSESolutions.com) parts of ∆BCA will be :
(i) ∠E ↔ ∠C
(ii) \(\overline { EF }\) ↔ \(\overline { CA }\)
(iii) ∠F ↔ ∠A
(iv) \(\overline { DF }\) ↔ \(\overline { BA }\)

Short Answer Type Questions

Question 1
In figure AB = AC and D is mid point of BC.
(i) Write three pairs of (RBSESolutions.com) equal parts in ∆ADB and ∆ACD.

(ii) Is ∆ADB = ∆ADC ?
Give reason.
(iii) What is relation between ∠B and ∠C?
Solution:
(i) In ∆ADB and ∆ADC
AD = AD (common)
AB = AC (given)
and DB = DC (∵ D is mid point of BD)
(ii) By S.S.S. rule of congruency.
∆ADB ≅ ∆ADC
(iii) ∠B = ∠C (CPCT)

Question 2
Is ∆ABC ≅ ∆DEF ? Write their (RBSESolutions.com) corresponding angles.

Solution:
In given figure ∆ABC and ∆DEF
AB = EF = 7 cm, 5C = DF = 3.9 cm,AC = DF = 6.5 cm
Clearly A is corresponding of F.,
B is corresponding (RBSESolutions.com) of E and C is corresponding of D
∴ ∠A = ∠F, ∠B = ∠E and ∠C = ∠D
∴ ∆ABC ≅ ∆FED.

Question 3
In figure, BD and CEy are altitudes of ∆ABC and ∆BD = CE.
(i) Write three pairs of equal parts in ∆CBD and ∆BCE.
(ii) Is ∆CBD ≅ ∆BCE ? Why and why not?
(iii) Is ∠DCB ≅ ∠EBC ? Why and why not?

Solution:
(i) Three equal (RBSESolutions.com) parts in ∆CBD and ∆BCE are
CB = BC (common)
∠CDB = ∠BEC (each 90°)
and BD = CE (given)
(ii) From R.H.S. condition of congruency
∆CBD ≅ ∆BCE
(iii) Yes, ∠DCB = ∠EBC
(∵ corresponding angles of congruent triangles are equal)

Long Answer Type Questions

Question 1
Divide a square sheet in (RBSESolutions.com) two triangles of equal area so that they are congruent
Solution:
∆ABC of = \(\frac { 1 }{ 2 }\) x BC x AB
= \(\frac { 1 }{ 2 }\) x 4 x 4 = 8 sq unit

and area of ∆DCA
= \(\frac { 1 }{ 2 }\) x DC x DA
= \(\frac { 1 }{ 2 }\) x 4 x 4 = 8 sq unit
∴ Area of ∆ABC = Area of ∆CDA
In ∆ABC and ∆CDA
AB = CD, ∠B =∠D and AC = AC(common)
∴ By RHS rule of congruency, ∆ABC ≅ ∆CDA

Question 2
The lengths of sides of triangles (RBSESolutions.com) shown in the following figures. Using SSS condition of congruency find which of the pairs are congruent, in condition of congruency, write in symbolic form.


Solution:
(i) In ∆ABC and ∆PQR
AB = PQ= 1.5 cm
BC = QR = 2.5 cm
CA = RP = 2.2 cm
By S.S.S. condition (RBSESolutions.com) of congruency ∆ABC ≅ ∆PQR

(ii) In ∆DEFand ∆LMN , EF ≠ MN
∴ These triangles are not congruent.

(iii) In ∆ABCand ∆PQR
BC ≠ QR
∴ These triangles are not congruent.

(iv) In ∆ADBand ∆ADC
AD = AD (common)
DB = DC = 2.5 cm
and BA = CA = 3.5 cm
In S.S.S. condition (RBSESolutions.com) of congruency , ∆ADB ≅ ∆ADC.

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