CBSE 7th Standard Mathematics Congruence of Triangles Model Questions Papers Study Material - QB365 Set A | QB365

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CBSE 7th Standard Mathematics Congruence of Triangles Model Questions Papers Study Material - QB365 Set A

Published on: 31/10/2025

Question Set A

CBSE 7th Standard Mathematics Congruence of Triangles Model Questions Papers Study Material - QB365

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Std: 7th Standard CBSE - Mathematics

chapter: Congruence of Triangles - Model Questions Papers

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Questions:

Generic 2

5 x 2 = 10

In the given figure, the two triangles are congruent. The corresponding parts are marked. We can write \(Δ\)RAT\(≅\ ?\)

If ΔABC ≅ ΔDEF, then find the values of AB and mㄥE.

By applying SAS congruence rule, you want to establish that ΔPQR ≅ ΔFED. It is given that PQ = FE and RP= DF. What additional information is needed to establish the congruence?

If ΔDEF ≅ ΔPQR, then corresponding congruent part(s) of the triangle is \(\bar { EF } \).

If ΔDEF ≅ ΔPQR Write the part(s) of ΔPQR that corresponds to ㄥF

Generic 3

5 x 3 = 15

In the following figures, lengths of the sides of the triangles are indicated. By applying SSS congruence rule, state which pairs of triangles are congruent? In case of congruent triangles, write the result in symbolic form.

ΔPQR is congruent to ΔLMN, mㄥP=7a, mㄥL = (4a+15) and ㄥP, ㄥQ are complementary. Find the value of a.

ABC is an isosceles triangle with AB = AC and AD is one of its altitudes (see the figure).
(i) State the three pairs of equal parts in ΔADB and ΔADC
(ii) Is ㄥB = ㄥC? Why or why not?
(iii) Is BD = CD? Why or why not?

10.

When two triangles, say ABC and PQR are given, there are in all, six possible matchings or correspondences. Two of them are
(i) ABC ↔️ PQR (ii) ABC ↔️ QRP
Find the other four correspondences by using two cut outs of triangles. Will all these correspondences lead to congruence?

Multiple Choice Question

5 x 1 = 5

11.

Which congruence criterion do you use in the following?
Given, ZX = RP, RQ =ZY, ㄥPRQ = ㄥXZY. So, ΔPOR ≅ ΔXYZ

(a)

ASA rule

(b)

SSS rule

(c)

RHS rule

(d)

SAS rule

12.

By applying ASA congruence rule, it is to be established that ΔABC ≅ ΔQRP and it is given that BC = RP. What additional information is needed to establish the congruence?

(a)

AB = OR and ㄥC = ㄥP

(b)

ㄥB = ㄥR and ㄥA =ㄥQ

(c)

ㄥB = ㄥR and ㄥC = ㄥP

(d)

None of the above

13.

Which of the following rule of congruency say that ΔABC ≅ ΔPQR

(a)

SSS

(b)

RHS

(c)

ASA

(d)

SAS

14.

By which of the following criterion, the two triangles cannot be proved congruent?

(a)

AAA

(b)

SSS

(c)

SAS

(d)

ASA

15.

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

(a)

RHS congruence criterion

(b)

ASA congruence criterion

(c)

SAS congruence criterion

(d)

AAA congruence criterion

Fill up / 1 Marks

5 x 1 = 5

16.

If ΔABC ≅ ΔPQR, ㄥA=60⁰ and ㄥC=50⁰, then find the value ㄥQ. = ......

17.

In right angled ΔABC and ΔPQR, hypotenuse and one side is same in both triangles, then ΔABC .... ΔPQR

18.

If ΔABC ≅ ΔPQR, then QR= _____

19.

If ΔABC ≅ ΔPQR, then ㄥB= _____

20.

In Δ KMN, the included angle between MN and NK is _____

True or False

5 x 1 = 5

21.

If ΔABC is an isosceles triangle, where AB = AC and D is mid-point of BC, then ΔABD ≌ ΔACD.

(a)

False

(b)

True

22.

There are six elements in a triangle.

(a)

False

(b)

True

23.

In ΔABC and ΔPQR, AB =PQ, BC = QR and ㄥB = ㄥQ, then ΔABC ≅ ΔPQR by the SAS criterion.

(a)

False

(b)

True

24.

If hypotenuse and an acute angle of one right angled triangle are equal to the hypotenuse and an acute angle of another right angled triangle, then the triangles are congruent.

(a)

False

(b)

True

25.

If two sides and one included angle of a triangle are equal to the two sides and one included angle of another triangle, then the two triangles are congruent.

(a)

False

(b)

True

Generic 5

1 x 5 = 5

26.

If ΔABC ≅ ΔPQR, where ㄥA=(3x-10) and ㄥP=(x+50), then the value of ㄥC, where ㄥC=x.

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Answers Key:

Generic 2

5 x 2 = 10

In \(Δ\)RAT and \(Δ\)WON, we have
RA = WO [from the given figure]
\(\angle RAT=\angle WON\) [from the given figure]
AT = ON [from the given figure]
So, by SAS congruence rule, two triangles are congruent.
The correspondence is \(A↔️O,\ R↔️W,\ T↔️N.\)
In symbolic form, \(Δ\)RAT \(≅Δ\) WON

AB=3.5 mm, mㄥE =90⁰

Here, we want to establish that
ΔPQR ≅ ΔFED [by SAS congruence rule]
Given that, PQ = FE and RP = DF
So, the additional information needed to establish the congruence is ㄥP = ㄥF.

\(\bar { EF } \leftrightarrow \bar { QR } \).

If ΔDEF ≅ ΔPQR, then corresponding congruent part(s) of the triangle is ㄥF ↔️ ㄥR

Generic 3

5 x 3 = 15

In ΔABD and ΔADC, we have
AB= AC =35 cm, BD= DC = 25 cm and AD = AD [common]
Therefore, the three sides of MBD are equal to three sides of ΔADC.
So, two triangles are congruent by SSS congruence rule.
From the above equality relations, we have
A ↔️ A, B ↔️ C, and D ↔️ D
In symbolic form, ΔABD ≅ ΔACD

In ΔABC and ΔPQR, we have
AC = PR = 5 cm, BC = PQ = 4 cm
But AB # QR [∵ 2 cm # 2.5 cm]
So, SSS congruence rule is not applicable.
Hence, ΔABC and ΔPQR are not congruent.

x = 5 and HJ = 25

Given, ABC is an isosceles triangles with AB = AC and AD is one of its altitude.
(i) Three pairs of equal parts in ΔADB and ΔADC are
ㄥADB = ㄥADC = 90° [given]
AB=AC [given]
AD=AD [common]
(ii) Yes, in ΔADB and ΔADC, we have
ㄥADB= ㄥADC [given]
AB = AC [given]
AD = AD [common]
Therefore, by RHS congruence rule rwo angles are congruent, the correspondence is A ↔️ A, D ↔️ D, B ↔️ C.
In symbolic form, ΔADB ≅ ΔADC
We know that, the corresponding parts of two congruent triangles are equal.
∴ ㄥ B= ㄥC
(iii) Yes, since ΔADB ≅ ≅ ADC
We know that, corresponding parts of rwo congruent triangles are equal i.e. BD = CD.

10.

In Δ ABC and Δ PQR, there are side possible matchings or correspondences. Out of them, four correspondences are as follow:
(i) ABC ↔️ PRQ
(ii) ABC ↔️ RPQ
(iii) ABC ↔️ RQP
(iv) ABC ↔️ QPR
Yes, all these correspondences may lead to congruence.

Multiple Choice Question

5 x 1 = 5

11.