# Selina Solutions Class 9 Mathematics Solutions for Exercise 9(B) in Chapter 9 - Chapter 9- Triangles [Congruency in Triangles]

Question 11 Exercise 9(B)

The following figure shows a triangle ABC in which AB=AC. M is a point on AB

and N is a point on AC such that BM=CN.

Prove that:

(i) AM=AN

(ii) 𝚫AMC ≅ 𝚫ANB

(iii) BN=CM

(iv) 𝚫BMC ≅ 𝚫CNB

Answer:

Solution

Video transcript
"hello students my name is pramit singh and i welcome you all to leader learning homework one of india's best online classes now today in this video we have a question that is based on the topic of congruent triangles the question says the falling figure shows a triangle abc in which a b is equal to ac that means this side is a b and this is ac they are equal basically they are isosceles triangle m is a point on a b and n is a point on ac these are the two points m and n such that bm this bm is equal to cn so prove that first part am is equal to n so starting from first in triangle bm's amc that means a m c triangle a m c and triangle a and b triangle a and b we have a b is equal to ac that is given a b is equal to ac that is given similarly we have bn is equal to cn that is also given now if you check if we subtract equation 2 that means this is equation 2 and this is equation 1. if you subtract a b minus b n a b minus a a b minus b m this is b m b m is equal to c n a b minus b m if you subtract a b minus c m b m what you will be getting you will be getting am and if you subtract a c minus c n what you will be getting a n so what we have to prove in the first part that we have proved now similarly com in the second part what we have triangle amc and triangle a and b a m c in triangle a m c and triangle a n b now which two sides are equal ac is equal to a b that is given similarly angle a is equal to angle a that is common angle so this is side angle a is equal to angle a common and third part is am is equal to n that we have proved now if you check we have side angle side so what what we have proved congruent that is angle triangle amc is congruent to triangle a and b so first part proof second part proof now third part if you check we have cm is equal to bn cm is where this is cm cm is equal to bn how that is based on cpct corresponding parts of congruent triangles now in the last part we have triangle bmc and triangle c and b so in triangle bmc and triangle c and b we have bm is equal to cn that is given second part we have bc is equal to bc common side this bc common base that means and the last part is cn is equal to bn cm is equal to pn cn we have already proved cm is equal to bn so again side triple s theorem we have proved triangle bmc is congruent to triangle c and b so we have proved all the four parts i hope you have understood the concept very clearly but still if you have any doubt do comment in the comment box and please like and subscribe our channel for lido thank you"
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