NCERT Solutions for Class 7 Maths Exercise 7.2 Chapter 7 Congruence of Triangles

NCERT Solutions for Class 7 Maths Exercise 7.2 Chapter 7 Congruence of Triangles in simple PDF are given here. Criteria for congruence of triangles and congruence among right-angled triangles are the two topics covered in this exercise of NCERT Solutions for Class 7. Students of Class 7 are suggested to solve NCERT Solutions for Class 7 Maths Chapter 7 Congruence to strengthen the fundamentals and be able to solve questions that are usually asked in the examination.

Download the PDF of NCERT Solutions For Class 7 Maths Chapter 7 Congruence of Triangles â€“ Exercise 7.2

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Exercise 7.1 Solutions

Access Answers to NCERT Class 7 Maths Chapter 7 â€“ Congruence of Triangles Exercise 7.2

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 = 90o

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 = 30o, âˆ B = 40o and âˆ C = 110o

In Î”PQR, âˆ P = 30o, âˆ Q = 40o and âˆ R = 110o

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 = 90o

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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