AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3

AP State Syllabus AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 Textbook Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 8th Lesson Congruency of Triangles Exercise 3

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3

Question 1.
In following pairs of triangles, fmd the pairs which are congruent? Also, write the criterion of congruence.
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 1

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 2
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 3
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 4
Solution:
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 1
AB = PR
∠B = ∠P
∠C = ∠Q
Now by angle sum property
∠A = ∠R
∴ By A.S.A, ΔABC ≅ ΔRPQ

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 2
ΔADB ≅ ΔCBD by A.S.A.
∠ABD = ∠CDB
DB = DB

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 3
AB = CD
∠A = ∠D
∠B = ∠C (by angle sum properly
By A.S.A
ΔABO ≅ ΔDCO

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 4
We can say whether the triangles are congruent or not, at least one pair of sides should be given equal.

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3

Question 2.
In the adjacent figure.
(i) Are ΔABC and ΔDCB congruent?
(ii) Are ΔAOB congruent to ΔDOC’?
Also identify the relation between corresponding elements and give reason for your answer.
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3 5
Solution:
i) yes.
∠ACB = ∠DBC
BC = BC
∠ABC = ∠DCB (by angle sum property)
∴ ΔABC ≅ ΔDCB (A.S.A)

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 3

ii) yes
∠A = ∠D
∠ABO = ∠DCO (angle sum property)
AB = DC [From (i)]
∴ ΔAOB ≅ ΔDOC (A.S.A)
Otherwise ΔAOB and ΔDOC are similar by A.A.A. In congruent triangles corresponding parts
are equal.