RD Sharma 2020 solution class 9 chapter 12 Congruent Triangles Exercise 12.4

Exercise 12.4

Page-12.57

Question 1:

In the given figure, it is given that AB =  CD and AD = BC. Prove that ΔADC ≅ΔCBA.
 

Answer 1:

It is given that

We have to prove that.

Now in triangles and we have

(Given)

(Given)

So (common)

Each side of is equal to .

Hence, by congruence criterion we have Proved.

Page-12.58

Question 2:

In a ΔPQR, if PQ =  QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively. Prove that LN = MN.

Answer 2:

It is given that 

and L, M, N are the mid points of sides, , and respectively.

 

We have to prove that

Now using the mid point theorem, we have

And

Similarly we have 

In triangle and we have

(Proved above)

(Proved above)

And (common)

So, by congruence criterion, we have 

And

Then

HenceProved.