Question

The given figure shows a triangle $ABC$ in which $AB=AC$. $M$ is a point on $AB$ and $N$ is a point on $AC$ such that $BM=CN$. Hence, $BN=CM$.

If the above statement is true, then mention answer as 1, else mention 0 if false.

Answer 1

$AB=AC$ (Given)
$BM=NC$ (Given)

Subtracting both the equations:
$AB-BM=AC-NC$
$⟹$ $AM=AN$.

Now, in $△$s, $ABN$ and $ACM$,
$AB=AC$ (given)
$AM=AN$ (Proved above)
$\angle A=\angle A$ (Common)
Thus, $△ABN\cong △ACM$ (by $SAS$ congruency)
Hence, $BN=CM$ (By $CPCT$).

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