Question

23.
In the given figure, the equal sides AB and AC of an isosceles triangle ABC are produced to N and
M, respectively such that AN = AM. Prove that MB = NC.
M​

Answer 1

Given : the equal sides AB and AC of an isosceles triangle ABC are produced to N and  M, respectively such that AN = AM.

To Find : Prove that MB = NC

Solution:

ABC isosceles triangle

AB = AC

=> ∠ABC  = ∠ACB

AN = AM

=> AN - AB = AM - AC

=>  BN = CM

∠NBC = 180° - ∠ABC

∠MCB = 180° - ∠ACB

∠ABC  = ∠ACB

=> ∠NBC  = ∠MCB

Comparing  ΔCBN &  ΔBCM

CB =  BC  ( common)

∠NBC =  ∠MCB

BN = CM

=> ΔCBN ≅  ΔBCM   ( SAS)

=> CN = MB

QED

Hence Proved

Learn More:

Triangle ABC is an isosceles triangle with AB= BC. Prove that ...

https://brainly.in/question/14774875

In the given figure, ABCD is a square and DCM isan equilateral ...

https://brainly.in/question/20366168

suppose ABC is an isosceles triangle with AB=AC;BD and CE are ...

https://brainly.in/question/1939503