Question

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

Answer 1

$B$ is the midpoint of $\overline{AC}\Rightarrow \overline{AB}=\overline{BC}$ .........$\left(1\right)$

$C$ is the midpoint of $\overline{BD}\Rightarrow \overline{BC}=\overline{CD}$ .....$\left(2\right)$

From eqns$\left(1\right)$ and $\left(2\right)$ we have

$\overline{AB}=\overline{BC}=\overline{CD}$

$\therefore \overline{AB}=\overline{CD}$