ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Ex 12.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1

Question 1.
If ΔABC and ΔDEF are congruent under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 1

Question 2.
If ΔDEF = ΔBCA, then write the part(s) of ΔBCA that correspond to
(i) ∠E
(ii) \(\bar { EF }\)
(iii) ∠F
(iv) \(\bar { DF }\)
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 2

Question 3.
In the figure given below, the lengths of the sides of the triangles are indicated. By using SSS congruency rule, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 3
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 4

Question 4.
In the given figure, AB = 5 cm, AC = 5 cm, BD = 2.5 cm and CD = 2.5 cm
(i) State the three pairs of equal parts in ΔADB and ΔADC
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 5
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 6

Question 5.
In the given figure, AB = AC and D is the mid-point of \(\bar { BC }\).
(i) State the three pairs of equal parts in ΔADB and ΔADC.
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 7
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 8

Question 6.
In the figure given below, the measures of some parts of the triangles are indicated. By using SAS rule of congruency, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 9
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 10

Question 7.
By applying SAS congruence rule, you want to establish that ΔPQR = ΔFED. If is given that PQ = EF and RP = DF. What additional information is needed to establish the congruence?
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 11

Question 8.
You want to show that ΔART = ΔPEN
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 12
(a) If you have to use SSS criterion, then you need to show
(i) AR = ……….
(ii) RT = ……….
(iii) AT = …………
(b) If it is given that ∠T = ∠N and you are to use the SAS criterion, you need to have
(i) RT = ………. and (ii) PN = ……….
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 13

Question 9.
You have to show that ΔAMP = ΔAMQ.
In the following proof, supply the missing reasons.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 14
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 15

Question 10.Solution:
In the given figure:
(i) State three pairs of equal parts in ΔPSR and ΔRQP.
(ii) Is ΔPSR = ΔRQP? Give reasons
(iii) Is PS = RQ? Why?
(iv) Is ∠S = ∠Q? Why?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 16
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 17

Question 11.
In the given figure, AB = DC and ∠ABC = ∠DCB.
(i) State three pairs of equal parts in AABC and ADCB.
(ii) Is ΔABC = ΔDCB? Give reasons.
(iii) Is AC = DB? Why?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 18
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 19

Question 12.
In the quadrilateral, AC = AD, and AB bisect ∠CAD.
(i) State three pairs of equal parts in ΔABC and ΔABD.
(ii) Is ΔABC = ΔABD? Give reasons.
(iii) Is BC = BD? Why?
(iv) Is ∠C = ∠D? Why?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 20
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1 21