Question

In figure given, we have $X$ and $Y$ are the midpoints of $AB$ and $BC$ and $AX=CY$. Show that $AB=BC$.

Answer 1

Given, $X$ is the midpoint of $AB$

So, $AX=BX$$⟹AB=2AX$

Again, $Y$ is the midpoint of $BC$

so, $BY=CY$$⟹BC=2CY$

And also, $AX=CY$

Now, $AB=2AX=2CY=BC$

So, $AB=BC$

Hence proved.