Chapter 4.1, Problem 9CE

To determine

ToProve : Prove that O is the midpoint of any segment shown in figure.

Answer to Problem 9CE

Since $BO=DO$ and $AO=CO$

So, O is the midpoint.

Explanation of Solution

Given information : Two triangle are congruent shown in the figure given below

  

Given that two triangle is congruent.

i.e. $\Delta ABO\cong \Delta CDO$

We know that when two triangles are congruent then their corresponding angles and sides are equal.

So, we have

  $BO=DO$ and $AO=CO$

Here AC and BD are two lines intersect at O.

and $BO=DO$ , $AO=CO$

This imply that O is the midpoint of line segment AC and BD