Question

If $B$ is the mid point of $\overline{AC}$ and $C$ is the mid point of $\overline{BD},$ where $A,B,C,D$ lie on a straight line, say why $AB=CD$ ?

Answer 1

Given, $A,B,C,D$ are collinear such that,

${}^{\prime }{B}^{\prime }$ as the mid point of $AC$

$\Rightarrow AB=BC⟶\left(1\right)$

Similarly, ${}^{\prime }{C}^{\prime }$ is the mid point of $BD$

$\Rightarrow BC=CD⟶\left(2\right)$

Now, combining $\left(1\right)$ & $\left(2\right)$ we can write

$AB=CD$