Question

A,B,C, and D are the points such that B is the mid-point of $\overline{AC}$ and C is the mid-point of $\overline{BD}$. Show that $\overline{AB}=\overline{BC}=\overline{CD}=\frac{1}{3}$ of $\overline{AD}$

Answer 1

Given

$B$ is the midpoint of $AC$

$\Rightarrow AB=BC$

C is the midpoint of BD

$\Rightarrow BC=CD$

$\Rightarrow AB=BC=CD$

From the given data

$AB+BC+CD=AD$

$AB+AB+AB=AD$

$3AB=AD$

$AB=\frac{1}{3}AD$

$\Rightarrow AB=BC=CD=\frac{1}{3}AD$