Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Congruency: Congruent Triangles Exercise 19 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, whether the pairs of triangles given in the following figures are congruent or not:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q1.1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 2

Question 2.
In the given figure, prove that:
∆ABD ≅ ∆ ACD
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 3

Question 3.
Prove that:
(i) ∆ABC ≡∆ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 4

Question 4.
Prove that:
(i) ∆ABD  ≡ ∆ACD
(ii) ∠B = ∠C
(iii) ∠ADB = ∠ADC
(iv) ∠ADB = 90°
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q4
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 5
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 6

Question 5.
In the given figure, prove that:
(i) ∆ACB ≅ ∆ECD
(ii) AB = ED
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q5
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 7

Question 6.
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 8

Question 7.
In the given figure, prove that: BD = BC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 9

Question 8.
In the given figure ;
∠1 = ∠2 and AB = AC. Prove that:
(i) ∠B = ∠C
(ii) BD = DC
(iii) AD is perpendicular to BC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 10

Question 9.
In the given figure prove tlyat:
(i) PQ = RS
(ii) PS = QR
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q9
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 11

Question 10.
(i) ∆ XYZ ≅ ∆ XPZ
(ii) YZ = PZ
(iii) ∠YXZ = ∠PXZ
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q10
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 12

Question 11.
In the given figure, prove that:
(i) ∆ABC ≅ ∆ DCB
(ii) AC=DB
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q11
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 13

Question 12.
In the given figure, prove that:
(i) ∆ AOD ≅ ∆ BOC
(ii) AD = BC
(iii) ∠ADB = ∠ACB
(iv) ∆ADB ≅ ∆BCA
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q12
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 14

Question 13.
ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:
(i) AD = BE
(ii)BD = CE
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q13
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 15

Question 14.
Use the informations given in the following figure to prove triangles ABD and CBD are congruent.
Also, find the values of x and y.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q14
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 16
Question 15.
The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ABD ≅ ∆ACD
(ii) AB=AC
(iii) ∠B = ∠C
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q15
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 17

Selina Concise Mathematics Class 7 ICSE Solutions