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
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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