Chapter 10 Congruent Triangles RD Sharma Solutions Exercise 10.4 Class 9 Maths
Chapter Name  RD Sharma Chapter 10 Congruent Triangles Exercise 10.4 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 10.4 Solutions
1. In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that Î”ADC ≅ Î”CBA.
Solution
Given that in the figure AB = CD and AD = BC.
We have to prove
Î”ADC ≅ Î”CBA
Now,
Now,
Consider Î”ADC and Î”CBA,
We have
AB = CD [Given]
BC = AD [Given]
And AC = AC [Common side]
BC = AD [Given]
And AC = AC [Common side]
So, by SSS congruence criterion, we have
Î”ADC ≅ Î”CBA
∴ Hence proved
2. In a Î”PQR, if PQ = QR and L, M and N are the mid  points of the sides PQ, QR and RP respectively. Prove that LN = MN.
Solution
Given that in Î”PQR, PQ = QR and L, M and N are mid  points of PQ, QR and RP respectively
We have to prove LN = MN.
Join L and M, M and N, N and L
We have
PL = LQ, QM = MR and RN = NP
[∵ L, M and N are mid  points of PQ, QR and RP respectively]
And also,
PQ = QR ⇒ PL = LQ = QM = MR = PQ/2 = QR/2 ...(1)
Using mid  point theorem, we have
MN  PQ and MN = (1/2)(PQ)
⇒ [MN = PL = LQ] ...(2)
Similarly, we have
LN  QR and LN = (1/2)(QR)
⇒ LN = QM = MR
From equation (1), (2) and (3), we have
PL = LQ = QM = MR = MN = LN
∴ LN = MN