SEBA Class 7 Mathematics Chapter 7 Congruence of Triangles

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SEBA Class 7 Mathematics Chapter 7 Congruence of Triangles

Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 7 General Maths Textual Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 7 Mathematics Chapter 7 Congruence of Triangles Solutions for All Subject, You can practice these here.

Congruence of Triangles

Chapter – 7

PART – I

Exercise – 7.1

1. Measures of sides of pairs of triangles are given in figure below. Show that the pairs are congruent. Mention the congruence criteria.

Ans: RHS Criterion.

Ans: SSS Criterion.

Ans: RHS Criterion.

Ans: RGS Criterion.

(e)

Ans: SSS Criterion.

Ans: SAS Criterion.

Ans: AAS Criterion.

Ans: AAS or ASA Criterion.

2. In fig (i) 

Prove that  ∆ADC ≌ ∆CВА

Ans: Given: 

To prove: ∆ADC ≌ ∆CВА

Proof: From ∆ADC and  ∆CВА

Proof that ∆PRQ ≌ ∆PSQ

Ans: From given ∆PRQ and ∆PSQ

4. In the figure below ∆ABC is a Isosceles triangle, where 

and  is its median. Prove that

Ans: In given figure ∆ABC 

and

5. ABC is a Isosceles triangle with and AD is its altitude.

(i) Write down three equal parts of ∆ADB and ∆ADC.

Ans: Three equal parts of ∆ADB and ∆ADC are ∠A = ∠C, AD = AD (Common side), BD = CD.

(ii) Is AABD = AADC? Give reason.

Ans: Yes, ∆ADB = ∆ADC because is a median.

(iii) Is ∠B = ∠C?

Ans: ∠B = ∠C, because ∆ADB = ∆ADC

(iv) give reasons?

Ans:  

6. In ∆ ABC, ∠A = 30° ∠C = 110° and in ∆ PQR, ∠P = 30°, ∠R = 110°, Is ∆ ABC ≅ ∆PQR?

Ans: Yes, ∆ ABC = ∆PQR, because ∠A = ∠P ∠C = 4 ∠R and (According to A-S-A Property).

7. In the figure bisects ∠A also, in ∆АВС, show that the angles opposite to equal sides are equal.

Ans: 

∆ ABD = ∆ADC [According to S-S-S and S – A -: Property] ∠B = ∠C

8. In ∆ABC, ∠B = ∠C,  and are bisectors o ∠B and ∠C respectively. Prove that

Ans: Given: In ∆ABC, ∠B = ∠C, and are bisectors of ∠B and∠C respectively.

 Prove that:

Proof: From ∆BCM and ∆BCL, ∠B = ∠C, is a common side, .

∴ ВСМ = ∆BCL (According to S-A-S Property)

∴    (Proved)

9. If the mid point M of the base is equidistant from the other two sides of a triangle ∆ABC then show that the triangle is isosceles.

Ans:

Given: If the mid point M of the base is equidistant from the other two sides of a ∆ABC

To show: 

Proof: From ∆BFM and ∆DCM, (∴ M is the mid point of BC)

(Given) 

<BFM = CDM = 90° 

∴ ∆BFM = ∆DCM 

∴ ∠B = ∠C

∴ (Showed)

10. In fig., Write down three equal parts of ∆ABC and ∆DAB. Show that-

(i)  ∆АВС ≅ ∆BAD

Ans: In fig, ans AB = AB (Common side), and DA = CB, ∠A = ∠B

∴ ∆ABC = ∆BAD [According to S-A-S Property) [Showed]

11. In the given figure BD and CE are two altitudes of ΔABC such that BD = CE.

(i) Write three equal parts of ΔBCD and ΔВСЕ

(ii) Is ΔCBD ≌ ΔBCE?

(iii) Is ∠DCB ≌ ∠EBC? If not, why?

Ans: In the given figure BD and CE are two altitudes of ∆ABC such that BD = CE.

(i) Three equal parts of ∆CBD and ∆BCE are ∠B = ∠C, ∠BEC = ∠BDC and BC = BC (Common side)

(ii) ∆CBD ≌ ∆BCE [According to A-A-S property]

(iii) ∠DCB = ∠EBC [∴  BD= CE]

12. In the given figure and . Show that, ∆ABC ≌ ∆CDA.

Ans: 

In the given figure and

Το show: ΔABC ≌ ∆CDA

Proof: From ∆ABC and ∆CDA, and (Common side). 

∆ ABC ≌ ∆CDA (According to S-S-S Property.)

Exercise – 7.2

Find out the correct statements of the following questions:

1. If in ∆ABC and ∆PQR, AB = 4 cm BC = 5 cm AC = 6 cm, PQ = 4 cm OR = 5 cm PR = 6 cm then:

(a) ∆ΑΒC ≌ ∆QRP

(b) ∆АВС ≌ ∆PQR

(c) ∆АВС ≌ ∆PRQ

(d) ∆ΑΒC ≌ ∆QPR

Ans: (b) ∆АВС ≌ ∆PQR

2. In ∆ABC, ∠A = 90° and then.

(a) ∠B = ∠C = 60°

(b) ∠B = ∠C = 30°

(c) ∠B = ∠C = 45°

(d) ∠B = ∠B = 50°

Ans: (c) ∠B = ∠C = 45°

3. The measure of each angle of an equilateral triangle-

(a) 60°

(b) 30°

(c) 45°

(d) 40°

Ans: (a) 60°

4. In the figure AB = CD, AD = CB and ∠DAB = ∠BCD then

(a) ∆ΑΒC ≌ ∆ADC

(b) ∆АВС ≌ ∆ACD

(c) ∆BAD ≌ ∆DCB

(d) ∆ΑΒC ≌ CAD

Ans: (c) ∆BAD ≌ ∆DCB

5. In ∆ABC and ∆PQR AB = 3.5 cm BC = 7.1cm AC = 5 cm. PQ = 7.1cm QR = 5 cm and PR = 3.5cm Which of the following statements is correct?

(a) ∆АВС ≌ ∆QRP

(b) ∆ΑΒC ≌ ∆PQR

(c) ∆ABC ≌ ∆RPO

(d) ∆ΑΒΟ ≌ ∆OPR

Ans: (c) ∆ABC ≌ ∆RPO

6. In ∆ABC and ∆DEF AB = 7cm BC = 5cm, ∠B = 50° DE = 5 cm EF = 7cm ∠E = 50° Under which condition, are the traingles congruent?

(a) SAS.

(b) RHS.

(c) ASA.

(d) SSS.

Ans: (a) SAS.

7. In ∆ABC and ∆PQR ∠B = ∠P = 90° and AB = RP Triangles are congruent if,

(a) AC = RQ

(b) ∠A = ∠P

(c) BC = QR

(d) ∠R = ∠C

Ans: (a) AC = RQ

৪. If ∆AB C cong ∠DEF and ∠A = 50°, ∠E = 85 ° then ∠C = ?

(a) 50°

(b) 45°

(c) 85°

(d) 40°

Ans: (b) 45°