Question

In figure, $X$ and $Y$ are the points on equal sides of $AB$ and $AC$ such that $AX=AY$. Show that $XC=BY$.

Answer 1

In $\Delta ABC$
$AB=AC$ (given)
and $AX=AY$ (given)
$AB–AX=AC–AY$
$BX=CY$ ….(i)
Now in $\Delta BXC$ and $\Delta BYC$
$BX=CY$ [from (i)]
$BC=BC$ (common)
$\angle B=\angle C$ (angle opp. to equal sides are equal)
$\Delta BXC=\Delta BYC$ (by SAS property)
$XC=BY$ (by c.p.c.t)
Hence proved.