Question

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

Answer 1

Verify the given statement

Given: $\text{B}$ is the mid point of $\mathrm{AC}$ , $\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}$lie on a straight line.

$\Rightarrow$ $\mathrm{AB}=\mathrm{BC}$ $...\left(\mathrm{i}\right)$

And $\mathrm{C}$ is the mid point of $\mathrm{BD}$

$\Rightarrow$ $\mathrm{BC}=\mathrm{CD}$ $...\left(\mathrm{ii}\right)$

From, $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$, we get;

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

$\Rightarrow$ $\mathrm{AB}=\mathrm{CD}$

Hence,it is proved that $\mathrm{AB}=\mathrm{CD}$ .