**Download NCERT Solutions for Class 7 Maths Chapter 7 – Congruence of Triangles**

### NCERT Solutions for Class 7 Maths Chapter 7 – Exercise 7.1

**1. Complete the following statements:**

**a) Two line segments are congruent if ___________.
**Answer : They have the same length.

**b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is ___________.
**Answer: 70°

**c) When we write ****∠** **A = ****∠****B, we actually mean ___________****.
**Answer: m∠ A = m∠B. That is, if two angles have the same measure, they are congruent.

**2. Give any two real-life examples for congruent shapes.**

Ex 1: Two coins of same value

Ex 2: Pages of a book

**3. If ∆ABC ****≅**** ∆FED under the correspondence ABC ↔ FED, write all th****e corresponding congruent parts of the triangles.**

Given: ∆ABC ≅ ∆FED

ABC ↔ FED

The corresponding congruent parts of the triangles are:

∠A ↔ ∠F

∠B ↔ ∠E

∠C ↔ ∠D

↔

↔

↔

**4. If ∆DEF ****≅**** ∆BCA, write the part(s) of ∆BCA that correspond t****o**

**i) ∠****E
**∠E ↔ ∠C

**ii)**

↔

**iii) ∠F
**∠F ↔ ∠A

**iv)**

↔

**Download NCERT Solutions for Class 7 Maths Chapter 7 – Congruence of Triangles**

### NCERT Solutions for Class 7 Maths Chapter 7 – Exercise 7.2

**1. Which congruence criterion do you use in the following?**

**a) ****Given: AC = DF **

**AB = DE
**

**BC = EF**

**So, ∆ABC**

**≅**

**∆DE**

**F**

SSS criterion is used to prove the congruency.

**b) ****Given: ZX = RP**

**RQ = ZY **

**∠****PRQ = ****∠****XZ****Y**** **

So, ∆PQR **≅**** ∆XY****Z**** **

SAS criterion is used to prove the congruency.

**c) ****Given: ****∠****MLN = ****∠****FG****H
**

**∠**

**NML =**

**∠**

**HF**

**G**

**ML = FG**

**So, ∆LMN**

**≅**

**∆GF**

**H**

ASA criterion is used to prove the congruency.

**d) Given: EB = DB
**

**AE = BC**

**∠**

**A =**

**∠**

**C = 90**

**°**

**So, ∆ABE**

**≅**

**∆CD**

**B**

RHS criterion is used to prove the congruency.

**2. You want to show that ∆ART ****≅**** ∆PEN****,**

**a) If you have to use SSS criterion, then you need to show**

(i) AR = PE

(ii) RT = EN

(iii) AT = PN

**b) If it is given that ****∠****T = ****∠****N and you are to use SAS criterion****, you need to have**

(i) RT = EN

(ii) PN = AT

**c) If it is given that AT = PN and you are to use ASA criterion, you need to have**

(i) ∠RTA = ∠ENP

(ii) ∠RAT = ∠EPN

**3. You have to show that ∆AMP ****≅**** ∆AMQ****.
**

**In the following proof, supply the missing reasons.**

Steps | Reasons |

i) PM = QM |
i)Given |

ii) ∠PMA = ∠QMA |
ii)Given |

iii) AM = AM |
iii)Common |

iv) ∆AMP ≅ ∆AMQ. |
iv)SAS Congruency rule |

**4. In ∆ABC, ****∠****A = 30° , ****∠****B = ****40° and ****∠****C = 110****° In ∆PQR, ****∠****P = 30° , ****∠****Q = 40° and ****∠****R = 110****° A student says that ∆ABC ****≅**** ∆PQR by AA****A congruence criterion. Is he justified? Why or why not?**

There is no such thing as AAA Congruence of two triangles.

In such a correspondence, one of them can be an enlarged copy of the other.

Hence ∆ABC ∆PQR

**5. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆RAT ****≅** **?**

Consider the given : RA = WO

∠RAT = ∠WON

AT = ON

SAS congruency is satisfied.

Therefore we can say that ∆RAT ≅ ∆WON

**6. Complete the congruence statement:**

**i) ∆BCA ****≅** **?**

Consider the ∆BCA and ∆BTA

Given: BC = BT (Given)

BA =BA (Common)

CA =TA (Given)

Thus, by SSS congruency ∆BCA ≅∆BTA

**ii) ∆QRS ****≅** **?**

Consider the ∆QRS and ∆TPQ

Given: QR = TP (Given)

RS = PQ (Given)

QS = TQ (Given)

Thus, by SSS congruency ∆QRS ≅ ∆TPQ

**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:**

**i) The triangles are congruent**

Consider the right-angle ∆ABC and ∆PQR

The area swept by both the triangles is 24cm^{2}

i.e Area of ∆ABC =

=

=

= 24 cm^{2}

Similarly, Area of ∆PQR =

=

=

= 24 cm^{2}

By SSS criterion, ∆ABC ≅ ∆PQR and their areas are equal.

**ii) The triangles are not congruent.**

Consider the ∆LMN and ∆XYZ

The area swept by both the triangles is 24cm^{2}

i.e Area of ∆LMN =2 x Area of ∆LON

= 2 x

= 2 x

= 2 x

= 24 cm^{2}

Similarly, Area of ∆XYZ =

=

=

= 24 cm^{2}

But, ∆LMN ≇ ∆XYZ even though their areas are equal.

In case of congruent triangles their perimeters are equal (by SSS criterion), and in case of incongruent triangles, their perimeters are not equal.

Note: The lengths of the hypotenuse of all the right-angled triangles are found by Pythagoras Theorem.

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

Consider the ∆ABC and ∆XYZ

∠A = ∠X

∠B =∠Y

∠C = ∠Z

BC = YZ

AC =XZ

But the length of side AB ≠ XY

Therefore ∆ABC ≇ ∆XYZ

**9. If ∆ABC and ∆PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?**

Given: ∆ABC ≅ ∆PQR

∠ABC = PQR = 90^{o}

∠ACB = ∠PRQ

Therefore, the additional pair of corresponding part should be a side, say BC = QR

Thus, the ASA criterion is used to prove the congruency.

**10. Explain, why ∆ABC ****≅**** ∆FED****.**

Given: ∠ABC = ∠FED = 90^{o
}BC = ED

∠BAC = ∠EFD

By RHS criterion, ∆ABC ≅ ∆FED.

**Download NCERT Solutions for Class 7 Maths Chapter 7 – Congruence of Triangles**

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