Math, asked by geya34, 11 months ago


AB, AC are the equal sides of an isosceles triangle ABC and L,M, N are mid points
of the sides AB,BC, CA respectively. Show that BN=CL

Answers

Answered by bhagyashreechowdhury
0

If AB = AC of triangle ABC and L, M & N are midpoints of sides AB,AC & BC then BN = CL due to CPCT.

Step-by-step explanation:

It is given that,

L is the midpoint of AB i.e., AL = BL = ½ AB

M is the midpoint of BC i.e., BM = CM = ½ BC

N is the midpoint of CA i.e., AN = CN = ½ AC

Also, AB = AC [equal sides of the given isosceles ∆ABC] ….. (i)

⇒ ½ AB = ½ AC

AL = AN ….. (ii)

Now, consider ∆ABN and ∆ACL, we have  

AB = AC ….. [from (i)]

∠A = ∠A ….. [common angle]

AL = AN ….. [from (ii)]

By SAS congruence, ∆ABN ≅ ∆ACL

We know that when two triangles are congruent to each other then all of their corresponding angles and sides must be equal.

BN = CL  

Hence proved

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