NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles are given here. Students can either practice online or download these files and practice different types of questions related to this chapter and thereby achieve maximum marks in their examinations. The relation of two objects being congruent is called congruence. Subject experts prepare these NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles carefully, without any mistakes.

Chapter 7 â€“ Congruence of Triangles contains 2 exercises. Let us have a look at some of the concepts discussed in this chapter.

- Congruence of Plane Figures
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Triangles
- Criteria For Congruence of Triangles
- Congruence Among Right-Angled Triangles

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Exercise 7.1 Page: 137

**1. Complete the following statements:**

**(a) Two line segments are congruent if ___________.**

**Solution:-**

Two line segments are congruent if they have the same length.

**(b) Among two congruent angles, one has a measure of 70 ^{o}; the measure of the other angle is ___________.**

**Solution:-**

Among two congruent angles, one has a measure of 70^{o}; the measure of the other angle is 70^{o}.

Because, if two angles have the same measure, they are congruent. Also, if two angles are congruent, their measure are same.

**(c) When we write âˆ A = âˆ B, we actually mean .**

**Solution:-**

When we write âˆ A = âˆ B, we actually mean m âˆ A = m âˆ B.

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

**Solution:-**

The two real-life example for congruent shapes are,

(i) Fan feathers of same brand.

(ii) Size of chocolate in the same brand.

(iii) Size of pens in the same brand

**3. If Î”ABC â‰… Î”FED under the correspondence ABC â†” FED, write all the corresponding congruent parts of the triangles.**

**Solution:-**

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

All the corresponding congruent parts of the triangles are,

âˆ A â†” âˆ F, âˆ B â†” âˆ E, âˆ C â†” âˆ D

Correspondence between sides:

**4. If Î”DEF â‰… Î”BCA, write the part(s) of Î”BCA that correspond to**

**(i) âˆ E (ii) (iii) âˆ F (iv) **

**Solution:-**

From above the figure we can say that,

The part(s) of Î”BCA that correspond to,

(i) âˆ E â†” âˆ C

(ii)

(iii) âˆ F â†” âˆ A

(iv)

Exercise 7.2 Page: 149

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

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

**AB = DE**

**BC = EF**

**So, Î”ABC â‰… Î”DEF**

**Solution:-**

By SSS congruence property:- Two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

Î”ABC â‰… Î”DEF

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

**RQ = ZY**

**âˆ PRQ = âˆ XZY**

**So, Î”PQR â‰… Î”XYZ**

**Solution:-**

By SAS congruence property:- Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

Î”ACB â‰… Î”DEF

**(c) Given: âˆ MLN = âˆ FGH**

**âˆ NML = âˆ GFH**

**âˆ ML = âˆ FG**

**So, Î”LMN â‰… Î”GFH**

**Solution:-**

By ASA congruence property:- Two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Î”LMN â‰… Î”GFH

**(d) Given: EB = DB**

**AE = BC**

**âˆ A = âˆ C = 90 ^{o}**

**So, Î”ABE â‰… Î”ACD**

**Solution:-**

By RHS congruence property:- Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.

Î”ABE â‰… Î”ACD

**2. You want to show that Î”ART â‰… Î”PEN,**

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

**(i) AR = (ii) RT = (iii) AT =**

** **

**Solution:-**

We know that,

SSS criterion is defined as, two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

âˆ´ (i) AR = PE

(ii) RT = EN

(iii) AT = PN

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

**(i) RT = and (ii) PN =**

** **

**Solution:-**

We know that,

SAS criterion is defined as, two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

âˆ´ (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) ? (ii) ? **

**Solution:-**

We know that,

ASA criterion is defined as, two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Then,

(i) âˆ ATR = âˆ PNE

(ii) âˆ RAT = âˆ EPN

**3. You have to show that Î”AMP â‰… Î”AMQ.**

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

Steps |
Reasons |

(i) PM = QM |
(i) â€¦ |

(ii) âˆ PMA = âˆ QMA |
(ii) â€¦ |

(iii) AM = AM |
(iii) â€¦ |

(iv) Î”AMP â‰… Î”AMQ |
(iv) â€¦ |

**Solution:-**

Steps | Reasons |

(i) PM = QM | (i) From the given figure |

(ii) âˆ PMA = âˆ QMA | (ii) From the given figure |

(iii) AM = AM | (iii) Common side for the both triangles |

(iv) Î”AMP â‰… Î”AMQ | (iv) By SAS congruence property:- Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other. |

**4. In Î”ABC, âˆ A = 30 ^{o}, âˆ B = 40^{o} and âˆ C = 110^{o}**

**In Î”PQR, âˆ P = 30 ^{o}, âˆ Q = 40^{o} and âˆ R = 110^{o}**

**A student says that Î”ABC â‰… Î”PQR by AAA congruence criterion. Is he justified? Why or Why not?**

**Solution:-**

No, because the two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be enlarged copy of the other.

**5. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write Î”RAT â‰… ?**

**Solution:-**

From the given figure,

We may observe that,

âˆ TRA = âˆ OWN

âˆ TAR = âˆ NOW

âˆ ATR = âˆ ONW

Hence, Î”RAT â‰… Î”WON

**6. Complete the congruence statement:**

**Î”BCA â‰… Î”QRS â‰…**

**Solution:-**

First consider the Î”BCA and Î”BTA

From the figure, it is given that,

BT = BC

Then,

BA is common side for the Î”BCA and Î”BTA

Hence, Î”BCA â‰… Î”BTA

Similarly,

Consider the Î”QRS and Î”TPQ

From the figure, it is given that

PT = QR

TQ = QS

PQ = RS

Hence, Î”QRS â‰… Î”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:-**

**(ii)**

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In the above figure, Î”ABC and Î”DEF have equal areas.

And also, Î”ABC â‰… Î”DEF

So, we can say that perimeters of Î”ABC and Î”DEF are equal.

**(ii) **

In the above figure, Î”LMN and Î”OPQ

Î”LMN is not congruent to Î”OPQ

So, we can also say that their perimeters are not same.

**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:- **

Let us draw triangles LMN and FGH.

In the above figure, all angles of two triangles are equal. But, out of three sides only two sides are equal.

Hence, Î”LMN is not congruent to Î”FGH.

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

**Solution:-**

By observing the given figure, we can say that

âˆ ABC = âˆ PQR

âˆ BCA = âˆ PRQ

The other additional pair of corresponding part is BC = QR

âˆ´ Î”ABC â‰… Î”PQR

**10. Explain, why Î”ABC â‰… Î”FED**

**Solution:-**

From the figure, it is given that,

âˆ ABC = âˆ DEF = 90^{o}

âˆ BAC = âˆ DFE

BC = DE

By ASA congruence property, two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Î”ABC â‰… Î”FED

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