NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

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Updated at 2021-05-07

NCERT solutions for class 7 Maths Chapter 7 Congruence Of Triangles Exercise 7.1

Q.1 Complete the following statements:
(a) Two line segments are congruent if _______ .
(b) Among the congruent angles, one has a measure of 70°, the measure of the other angle is _______ .
(c) When we write $\mathrm{?}A=\mathrm{?}B$, we actually mean

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) Two line segments are congruent if _they have the same length_ .
(b) Among the congruent angles, one has a measure of 70°, the measure of the other angle is _70°_ .
(c) $m\mathrm{?}A=m\mathrm{?}B$

Q.2 Give any two real life examples for congruent shapes.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Chocolate of the same packets.
Mobile phone of the same brand and model

Q.3 If $\mathrm{?}ABC?\mathrm{?}FED$ under the correspondence ABC ? FED, write all the corresponding congruent parts of the triangles.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Given: $\mathrm{?}ABC?\mathrm{?}FED$ and ABC? FED $?$ $\stackrel{?}{AB}?\stackrel{?}{FE},\stackrel{?}{BC}?\stackrel{?}{ED},\stackrel{?}{AC}?\stackrel{?}{FD}$
$\mathrm{?}A?\mathrm{?}F,\mathrm{?}B?\mathrm{?}E,\mathrm{?}C?\mathrm{?}D$

Q.4 If $\mathrm{?}DEF?\mathrm{?}BCA.$ Write the part of ABCA that correspond to
(i) $\mathrm{?}E$
(ii) $\stackrel{?}{E}F$
(iii) $\mathrm{?}F$
(iv) $\stackrel{?}{D}F$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Given: $\mathrm{?}DEF?\mathrm{?}BCA.$
(i) $\mathrm{?}E?\mathrm{?}C$
(ii) $\mathrm{?}F?\mathrm{?}A$
(iii) EF ? ZA
(iv) DF ? BA

NCERT solutions for class 7 Maths Chapter 7 Congruence Of Triangles Exercise 7.2

Q.1 Which congruence criterion do you use in the following?
(a) Given:
AC = DF
AB = DE
BC = EF
So, $\mathrm{?}ABC?\mathrm{?}DEF$

(b) Given:
ZX = RP
RQ = ZY
$\mathrm{?}PRQ=\mathrm{?}XZY$
So, $\mathrm{?}PQR?\mathrm{?}XYZ$

(c) Given: $\mathrm{?}MLN=\mathrm{?}FGH$
$\mathrm{?}NML=\mathrm{?}GFH$
ML = FG
So, $\mathrm{?}LMN?\mathrm{?}GFH$

(d) Given: EB = DB
AE = BC
$\mathrm{?}A=\mathrm{?}C=90°$
So, $\mathrm{?}ABE?\mathrm{?}CDB$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) $\mathrm{?}ABC?\mathrm{?}DEF$ (BY SSS rule)
(b) $\mathrm{?}PQR?\mathrm{?}XYZ$ (BY SAS rule)
(c) $\mathrm{?}LMN?\mathrm{?}GFH$ (BY ASA rule)
(d) $\mathrm{?}ABE?\mathrm{?}CDB$ (BY RHS rule)

Q.2 You want to show that $\mathrm{?}ART=\mathrm{?}PEN,$

(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
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) For SSS criterion, we need
(i) AR = PE
(ii) RT = EN
(iii) AT = PN
(b) For SAS criterion, we need
(i) RT = EN and
(ii) PN = AT
(c) For ASA criterion, we need
(i) $\mathrm{?}A=\mathrm{?}P$ (ii) $\mathrm{?}T=\mathrm{?}N$

Q.3 You have to show that $\mathrm{?}AMP?\mathrm{?}AMQ$. In the fallowing proof, supply the missing reasons.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Q.4 In ?ABC, $\mathrm{?}A=30°\mathrm{?}B=40°and\mathrm{?}C=110°$
In $\mathrm{?}PQR,\mathrm{?}P=30°,\mathrm{?}Q=40°and\mathrm{?}R=110°.$
A student says that $\mathrm{?}ABC=\mathrm{?}PQR$ by AAA congruence criterion.
Is he justified? Why or why not?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

The student is not justified because there is not criterion for AAA congruence rule.

Q.5 In the figure, the two triangles are congruent. The corresponding parts are marked. We can write $\mathrm{?}RAT?$ ?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

In $\mathrm{?}RATand\mathrm{?}WON$
AT=ON (Given)
AR=OW (Given)
$\mathrm{?}A=\mathrm{?}O$ (Given)
$?\mathrm{?}RAT?\mathrm{?}WON$(By SAS rule)

Q.6 Complete the congruence statement:

$\mathrm{?}BCA??\mathrm{?}QRS??$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(i) In $\mathrm{?}BCAand\mathrm{?}BTA$
BC = BT (Given)
$\mathrm{?}CBA=\mathrm{?}TBA\left(Given\right)$
BA= BA (Common)
$?\mathrm{?}BCA=\mathrm{?}BTA$ (by SAS rule)
(ii) In $\mathrm{?}QRSand\mathrm{?}TPQ$
RS = PQ (Given)
QS =TQ (Given)
PT= QR (Given)
$\mathrm{?}QRS?\mathrm{?}TPQ$ (by AAA rule)

Q.7 In a squared sheet, draw two triangles of equal areas such that:
(i) the triangles are congruent.
(ii) the triangle are not congruent.
What can you say about their perimeters?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(i)
i.e. perimeter of $\mathrm{?}ART$= Perimeter of $\mathrm{?}PEN$
(ii)
Perimeter of $\mathrm{?}ABC?$ Perimeter of $\mathrm{?}PQR$

Q.8 Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Q.9 If $\mathrm{?}ABCand\mathrm{?}PQR$ are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

In $\mathrm{?}ABCand\mathrm{?}PQR$
$\mathrm{?}ABC=\mathrm{?}PQR$
$\mathrm{?}BCA=\mathrm{?}PRQ$
The other additional pair of corresponding part is BC = QR
$?\mathrm{?}ABC?\mathrm{?}PQR$

Q.10 Explain, why $\mathrm{?}ABC?\mathrm{?}FED$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

In $\mathrm{?}ABCand\mathrm{?}FED$
$\mathrm{?}B=\mathrm{?}E=90°$ (Given)
$\mathrm{?}A=\mathrm{?}F$ (Given)
$?\mathrm{?}A+\mathrm{?}B=\mathrm{?}E+\mathrm{?}F$
$180°–\mathrm{?}C=180°–\mathrm{?}D$
[Angle sum property of triangles]
$?\mathrm{?}C=\mathrm{?}D$
BC = ED (Given)
$?\mathrm{?}ABC=\mathrm{?}FED$ (By ASA rule)

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