The given figure shows a triangle $A B C$ in which $A B = A C$ . $M$ is a point on $A B$ and $N$ is a point on $A C$ such that $B M = C N$ . Hence, $B N = C M$ .
If the above statement is true, then mention answer as 1, else mention 0 if false.

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Solution

$A B = A C$ (Given)
$B M = N C$ (Given)

Subtracting both the equations:
$A B - B M = A C - N C$
$⟹$ $A M = A N$ .

Now, in $△$ s, $A B N$ and $A C M$ ,
$A B = A C$ (given)
$A M = A N$ (Proved above)
$∠ A = ∠ A$ (Common)
Thus, $△ A B N ≅ △ A C M$ (by $S A S$ congruency)
Hence, $B N = C M$ (By $C P C T$ ).

Therefore, the statement is true and $1$ is the answer

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State true or false.

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