GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

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Gujarat BoardĀ GSEB Textbook Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 1.
Which congruence criterion do you use in the following?
(a) Given:
AC = DF
AB = DE
BC = EF
So, āˆ†ABC ≅ āˆ†DEF
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 1

(b) Given:
ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, āˆ†PQR = āˆ†XYZ
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 2

(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, āˆ†LMN ≅ āˆ†GFH
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 3

(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, āˆ†ABE ≅ āˆ†CDB
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 4
Solution:
(a) SSS congruence criterion
(b) SAS congruence criterion
(c) ASA congruence criterion
(d) RHS congruence criterion

GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 2.
You want to show that āˆ†ART ≅ āˆ†PEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR =
(ii) RT =
(iii) AT =

(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 5

(c) If it is given that AT = PN and you are to use ASA criterion, you need to have P
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 6
(i) ∠ATR =
(ii) ∠TAR =
Solution:
Here āˆ†ART ≅ āˆ†PEN
∓ A ↔ P, R ↔ E and T ↔ N

(a) (i) AR = PE
(ii) RT = EN
(iii) AT = PN

(b) ∵ ∠T = ∠N
(i) RT = EN
(ii) PN = AT

(c) (i) ∠ATR = ∠PNE
(ii) ∠TAR = ∠NPE

Question 3.
You have to show that āˆ†AMP ≅ āˆ†AMQ. In the following proof, supply the missing reasons.
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 8
Solution:
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 9

Question 4.
In āˆ†ABC, ∠A = 30°, ∠B = 40° and ∠C = 110°. In āˆ†PQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°. A student says that āˆ†ABC ≅ APQR by AAA congruence criterion. Is he justified? Why or why not?
Solution:
No, he is not justified.
Because AAA is not a congruence criterion.

GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 5.
In the figure, the two triangles are congruent. The corresponding parts are marked. We can write āˆ†RAT ≅?
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 10
Solution:
We have \(\left.\begin{array}{l}
\mathrm{O} \leftrightarrow \mathrm{A} \\
\mathrm{N} \leftrightarrow \mathrm{T} \\
\mathrm{W} \leftrightarrow \mathrm{R}
\end{array}\right\}\) ⇒ āˆ†RAT ≅ āˆ†WON

Question 6.
Complete the congruence statement:
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 11
Solution:
(i) We have:
\(\left.\begin{array}{l}
A \leftrightarrow A \\
B \leftrightarrow B \\
T \leftrightarrow C
\end{array}\right\} \Rightarrow \Delta B C A \cong \Delta B T A\)

(ii) \(\left.\begin{array}{l}
R \leftrightarrow P \\
Q \leftrightarrow T \\
S \leftrightarrow Q
\end{array}\right\} \Rightarrow \Delta Q R S \cong \Delta T P Q\)

Question 7.
In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent.
What can you say about their perimeters?
Solution:
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 12
(i) Area of āˆ†ABC = \(\frac { 1 }{ 2 }\) x 4 x 3 = 6 sq. cm
Area of āˆ†CDE = \(\frac { 1 }{ 2 }\) x 4 x 3 = 6 sq. cm
Perimeter of āˆ†ABC = (3 + 4 + 5) cm = 12 cm
Perimeter of āˆ†CDE = (3 + 4 + 5) cm = 12 cm
The two triangles are congruent.
[Perimeter of āˆ†ABC] = [Perimeter of āˆ†CDE]

(ii) Area of āˆ†PQR = Area of āˆ†PRS
Perimeter of āˆ†PQR = (3 + 4 + 5) cm = 12 cm
Perimeter of āˆ†PRS = (4 + 3.5 + 4) cm = 1.5 cm
The two triangles are not congruent.
[Perimeter of āˆ†PQR] ≠ [Perimeter of āˆ†PRS]

GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 8.
Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.
Solution:
A pair of triangle with 3 equal angles and two equal sides are non-congruent are as follows:
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 13
āˆ†ABC and āˆ†DEF are not congruent as any two sides and angle included between these two sides of āˆ†ABC is not equal to the corresponding two sides and included angle of āˆ†DEF.

Question 9.
If āˆ†ABC and āˆ†PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 14
Solution:
Here āˆ†ABC ≅ āˆ†PQR
∓ A ↔ P, B ↔ Q and C ↔ R
Two angles ∠B and ∠C of āˆ†ABC are respectively equal to two angles ∠Q and ∠R of āˆ†PQR.
∓ BC = QR
We use the ASA congruence criterion

GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 10.
Explain, why āˆ†ABC ≅ āˆ†FED.
GSEB Solutions Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 15
Solution:
∵ ∠A = ∠F (Given)
∓ ∠C = ∠D (Third angles are equal)
Also, BC = ED (Given)
Two angles (∠B and ∠C) and included side BC of āˆ†ABC are respectively equal to two angles (∠E and ∠D) and the included side ED of
∓ āˆ†ABC ≅ āˆ†FED.

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