Answer :
Answer:
Yes you're correct and I used similar concept in your previous question.
Step-by-step explanation:
Here's even a simpler way to understand this problem or solve the proof:
Given:
[tex]\bullet\ \text{$\overline{AB}\cong\overline{XY}$ or AB = XY}[/tex]
[tex]\bullet\ \text{O is the midpoint of $\overline{AB}$ and $\overline{XY}.$}[/tex]
Assumption:
[tex]\text{Let's assume that $\overline{AB}=\overline{XY}=10$ units.}[/tex]
To prove:
- [tex]\overline{AO}\cong\overline{XO}\text{$ or AO = XO}[/tex]
Proof:
1. Assume lengths:
[tex]\text{Assume $\overline{XY}=10$ units and $\overline{AB}=10$ units}[/tex]
2. Midpoint Definition:
[tex]\text{Since O is the midpoint of $\overline{AB}, $ the segment $\overline{AB}$ is divided into two}[/tex]
[tex]\text{equal parts:$}\\[/tex]
[tex]\overline{AO}=\overline{BO}=\dfrac{10}{2}=5\text{$ units}[/tex]
[tex]\text{$Similarly, since O is the midpoint of $\overline{XY}, $ the segment $\overline{XY}$ is divided }[/tex]
[tex]\text{$into two equal parts:}[/tex]
[tex]\overline{XO}=\overline{YO}=\dfrac{10}{2}=5\text{$ units}[/tex]
3. Conclusion:
From the above calculations, we see that:
[tex]\overline{AO}=\overline{XO}=5\text{$ units}[/tex]
Thus, we have proved that:
[tex]\overline{AO}\cong\overline{XO}[/tex]
So, essentially, when you divide two congruent line segments into equal parts, all the resulting segments are equal to each other.
This solution was just for your understanding, I recommend you not to write this in your original assignment.