AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2

AP State Syllabus AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 Textbook Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 8th Lesson Congruency of Triangles Exercise 2

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2

Question 1.
What additional information do you need to conclude that the two triangles given here under are congruent using SAS rule?
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 1
Solution:
We need
HG = TS
HJ = TR

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2

Question 2.
The map given below shows five different villages. Village M lies exactly halfway between the two pairs of villages A and B as well as and P and Q. What is the distance between village A and village P. (Hint: check if ΔPAM ≅ ΔQBM)
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 2
Solution:
Given that
AM = MB
PM = MQ
also ∠PMA = ∠QMB
∴ By S.A.S
ΔPMA ≅ ΔQMB
Now PA = BQ
(∵ Corresponding parts of congruent triangles are equal)
∴ PA = 4 km
i.e., Distance between the villages
A and P is 4 km.

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2

Question 3.
Look at the pairs of triangles given below. Are they congruent ? If congruent write the corresponding parts.
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 3
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 4
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 5
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 6

Solution:
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 3
AB=ST
AC = SR (given)
∠A = ∠S
∴ ΔABC ≅ ΔSTR (S.A.S)
Also ∠A = ∠S, ∠B = ∠T, ∠C = ∠R

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 4
From the figure,
FO = RO
OQ = OS
∠POQ = ∠ROS
∴ ΔPOQ ≅ ΔROS (SAS)
Also ∠P = ∠R, ∠Q = ∠S, and PQ = RS

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 5
From the figure, IAPBoardSoIJ
WD = OR
∠W= ∠R
WO = RD
∴ ΔDWO ≅ ΔORD
Also ∠EO = ∠OE; ∠WDO = ∠ROD; ∠WOD = ∠RDO

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 6
Here the two triangles ΔABC and ΔCDA are not congruent.

Question 4.
Which corresponding sides do we need to know to prove that the triangles are congruent using the SAS criterion?
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 2 7
Solution:
i) We need to know that AB = QR.
ii) We need to know that AD = AB.